LAST TIME REVISION MIXED - X
Compound interest
) A Man borrows Rs 400 at 4%p.a. C. I. If he repays Rs33 at the end of each year, Find the amount of loan outstanding at the beginning of the fourth year. Rs346.93
) A man puts Rs2000 in a bank in a fixed deposit account for a year. The bank pays C. I. at 8% per year, interest being paid half yearly. Find the amount of money to the man's credit after a year. Rs2163.20
) A man deposits Rs5000 in the State Bank account allowing C. I at 9/2% p.a. At the end of the first year transfer, he transfers the entire amount to a fixed deposit account for 2 years at 7% C.I p.a. Find the total amount of money in the name of the depositor at the end of the third year, nearest to a rupee. Rs5982
) The machinery of a certain factory is valued at Rs18400 at the end of 1999. If it is supposed to depreciate each year at 8% of the value at the beginning of the year, calculate the value of the machine at the end of 1988 and 2000. Rs20000, Rs16928
) The amount at CI which is calculated yearly on a certain sum of money is Rs 1250 in one year and Rs1375 in two years. Calculate the rate of interest. 10%
) The present population of a town is 75000. The population increases by 10% in the first year and decreases by 10% in the second year. Find the population after 2 years. 74250
) How much will Rs25000 amount in 2 years at CI, if the rates for the successive years by 4 and 5 percent per year. Rs27300
) A man borrows Rs2500 at 5% SI for 2 years. He immediately lends this money out at CI at the same rate and for the same time. What is his gain at the end of the 2 years, correct to the nearest rupee ? Rs6.25
) A man invested Rs45000 at 12% p.a. SI for 3 years. Find the difference in the intrest he would have earned, had he invested his money at CI, compounded annually, at the same rate for the same period. Rs2021.76
) A man borrowed Rs 5000 for 4 years under the following terms: 4% SI for first 5/2 years the interest being compounded semi-annually. Rs5836.66
) Find the sum on which the difference between the simple and compound interest for 5/2 years at 5% is Rs8.10. Rs1600
) Find the difference between the simple interest and the compound interest on a sum of Rs1000 for a period of 2 years at the rate of 10% p.a. Rs10
) A man lends Rs100 at 10.2% compound interest payable annually , and another man lends the same sum at 10% compounded interest but payable half yearly. Who will be gainer at the end of 1 year and by how much ? 2nd by 50 paise
) I invested Rs 8000 at simple interest for 3 years at 8% p.a. How much more would have been my return if I had invested it at compound interest at 15/2 p.a. Rs18.37
) Two partners Rahim and Karim together lend Rs1682 at 5%, compounded annually. The amount Rahim gets at the end of 3 years is the same as Karim gets at the end of 5 years. Determine the share of each in the principal . Rs882, Rs880
) A person left Rs163500 between his two sons aged 18 and 16 years such that they receive the same sum of money when they attain the age of 21. Find the sum left for each if the rate of interest t be 25/4%. S86700, Rs76800
) Divide Rs131144 into 3 parts such that if these 3 parts are lent at 5% compound interest for 2 years, 3 years and 4 years respectively the amount in each case is the same.
) Rs5000 is lent out for 2 years at 12% p.a CI. The interest is compounded annually. Find
a) the amount of the end of first year
b) the amount at the end of the second year.
c) the compound is to be paid.
Taxes
) Ravi bought a colour TV which was quoted at Rs15000. If the rate of sales tax is 12%, find the amount he has to pay for the TV. Rs16800
) A man has to pay Rs42.80 for his total purchases including sales tax calculated at 7% of the list price. Determine the list price of the articles purchased. Rs40
) Sheela purchased medicine costing Rs45 and has to pay Rs49.50 including sales tax. Determine the rate of sales tax. 10%
) A shopkeeper announces a discount of 5% the bill. If the market price of the TV. worth Rs 10000, how much the customer has to pay for the TV set if the rate of the sales tax is 6% ? Rs10070
) Anju buys a leather coat casting Rs990. The rate of sales tax is 10%. She tells the shopkeeper that he should reduce the price to such an extent that she has not to pay anything more than Rs990 including sales tax. Find the reduction needed in the cost price of the coat . Rs90
SHARE AND DIVIDEND
) Ravi invested Rs6250 in shares of a company paying 6% per annum. If he bought Rs25 share for Rs31.25 each, find his annual income from this investment. Rs300
) A man invests Rs4800 in shares of a company which was paying 8% dividend at the time when a Rs100 share cost Rs160. Find
a) his annual income from the shares. Rs240
b) the rate of interest he geta on his investment. 5%
) A person invested Rs8000 and Rs10000 in buying shares of two companies which later on declared dividend of 12% and 8% respectively. He collects the dividends and sells out his shares at a loss of 2% and 3% respectively. Find his total earning from the above transaction. Rs1300
) A person invested 20%, 30% and 25% of his savings in buying shares of three different companies A, B and C which declared dividend of 10%, 12% and 15% respectively. If his total income on account of dividends be Rs 2337.50, find his saving and the amount which he invested buying shares of each company.
) Mr Singh invested Rs8000 in 8%(Rs100) shares, selling at Rs80. After a year he sold these shares at Rs75 each and invested the proceeds in (Rs90) shares selling at Rs100 with a dividend of 12%. Calculate
a) his income from the first investment.
b) his income from the second investment .
c) the increased percentage return on his original investment.
INEQUATION IN ONE UNKNOWN
) If x ∈ {x : - 5 < x < 5 and x ∈I}, find the truth set of 7x²+ 2 ≥ x(7x +2). {-4,-3,-2,-1,1}
) P is the solution set of 8x -1 > 5x+2 and Q is the solution set of 7x- 2 ≥ 3(x + 6), where x ∈ N. Find P ∩Q. {5,6,7}
) Find solution set the inequation 12 + 6 x >0, where x is a negative integer. {-1}
) List the solution set of 30 - 4(2x - 1)< 30, given that x is a positive integer. {1,2,3...}
) if 1/9 < m/n < 1/8, where m and n are integers, write down any possible pair of values of m, n. 2,17
) Find the solution set of the inequation x + 5 ≤ 2x + 3, x ∈ R. Graph the solution set on the number line. {x:x ≥ 2, x ∈ R}
) The graph of a linear equation in x and y passes through (4,0) and (0,3). Find the value of k if the graph passes through (k, 1.5). -1,1
Graph
) Find graphically the vertices of the triangle whose sides have the equations 2y - x =8, 5y- x= 14 and y - 2x = 1 respectively. (6,4),(2,5),(1,3)
) Solve graphically the simultaneous equations x+ y= 7; 2x - 3y=9.
) Solve graphically the simultaneous equations 2x - y=9; 5x + 2y =27.
) Draw the graph of the equation y= 3x -4. From the graph read off
a) the value of y, when x= - 1. -7
b) the value of x when y = 5. 3
) a) What is the slope of the line 3x + 4y = 9 ?! -3/4
b) what is the slope of line 3x + 2 = 4 ? -3/2
) The graph of the equation y = 7x is parallel to the y-axis . State whether it is true or false. F
Quadratic equations
) Solve the following equation by Factorization Method:
a) 6x²+ 40= 31x. 8/3,5/2
b) √3 x²+10x+ 7√3 =0. -√3, 7√3/3
) In the following, determine whether the given quadratic equations have real roots and if so, find the roots
a) 25x²+ 20x +7=0. No
b) 9x²+ 7x -2=0. 2/9,-1
c) 2x²+ 5√3x +6=0. -√3/2,-2√3
d) 4x² - 20x +25=0. 5/2,5/2
) Factorize the given polynomials , wherever possible :
a) 21x² - x -2. (3x-1)(7x +2)
b) x²+ 4√2x +6. (x+√2)(x+ 3√2)
c) 2√2x²+ 4x +√2. √2(√2 x +1)
d) x²+ 2x + 6. (x+1 -√7)(x -1 +√7)
) Solve :
a) {(3x -1)/(2x+3)}⁴ - 5{(3x -1)/(2x+3)}²+4=0.
b) tˣ⁺¹ + 5²⁻ˣ = 5³ +1.
c) 2(x²+ 1/x²) - 3(x + 1/x) -1=0, x≠0.
d) √(3x²+ x+5)= x -3.
) The product of Rama's age(in years) 5 years ago with his age( in years) 9 years later is 15. Find Rama's present age.
) In a cricket match Kapil took one wicket less than twice the number of wickets taken by Ravi. If the product of the number of wickets taken by these two is 15, find the number of wickets taken by each.
) The sum of the squares of three consecutive natural number is 110. Determine the numbers.
) An integers when added to its square equal 90. Find all possible values of the integers.
) Some students planned a picnic. The budget for food was Rs24. Because four of the group failed to go, the cost of food to each member got increased by Rs1. How many students attended the picnic.
) if I had walked 1 kmph faster, I would have taken 10 minutes less to work 2 km. Find the rate of my walking.
) The length of a rectangle is 13/3 unit more than its breadth, and the area of the rectangle is 350 square units. Find the length of the rectangle.
) The perimeter of a rectangle is 82m and its area is 400 m². Find the breath of the rectangle.
) Aa segment AB and 2m length, is divided at C into two parts such that AC²= AB x CB. Find the length of part CB.
FACTOR THEOREM
) If x²- 3x - 4 is a factor of 2x³+ x²+ ax + b, find a and b.
) If (x -3) is a factor of 2x³+ ax² - 18x + 18, Show that (x +a) is a factor of x² -5x + 6.
) What should be added to x³ - 3x² - 10x + 24 so that (x -2) may be a factor.
RELATION AND FUNCTION
) Write down the domain and range of the relation (x,y): x= 3y and x and y are natural numbers less than 10.
) Given A={0, 1, 2, 3} and relation R defined on set A, as R={(x,y)∈ A x A : x = y } ; then
a) list the element of R
b) list the domain of R.
c) list the range of R.
) A set of right cylinder is such that each has a height of 7cm. The radius of the bases of the cylinders varies, the maximum radius being 21cm. Let r represent the relations and v the volume of cylinders, where r, b ∈ R.
a) Define the relation between r and v as a set of order pairs.
b) state the domain of the relation.
c) state the range of the relation.
d) Is the relation a function ?
) Given f: x --> x² -1 and g: x --> (x+1)/2, find f(3)/{f(3)+ g(3)}.
) A= {-2,-1,1,2} and f= {(x, 1/x), x ∈ A}
a) list the domain of f
b) list the range of f
c) Is f a function ?
) A certain jet plane has an average speed of 500 kmph. It can carry sufficient fuel for a 5 hour flight.
a) define the relation as a set , between the distance d( in km) and time t (in hours) for this plane .
b) state the domain of this relation.
c) state the range of this relation.
d) Is this relation a function.
) Let f be defined by f(x)= x/(x² + 1), x ∈ R find
a) f(1/x), x≠0
b) f(2x).
c) f(x -1).
d) f[(f -1)].
) A function f is defined by f={(x,y): x,y ∈N, y= 3x - 2 and x ≤ 4}.
a) list the set of ordered pairs of f.
b) Write down the range of f.
c) State, with a reason, whether f is one-one or many one.
d) State, with reason, whether f is into or onto.
) A set of positive integers is called S. What can be said about these integers if f(S)= S.
) If R(x)= (x+1)/x, find the value of
a) R(1).
b) R(-1).
c) R(1/2).
) Let f(x)= (2x²-1)/(x -2), x≠ 2, x ∈ R, find the value of f(5)/f(1/2).
) The function g is given by g(x)= 9 - x², where x∈ R the set of real numbers
a) Find the value of g(x).
b) Find the value of x for which g(x)=0.
) Given A={0, 1, 2,3} and relation R defined on the set A as
R={(x,y}∈ A x A : x=y}; then
a) List the elements of R
b) List the domain of R.
c) List the range of R.
) A mapping f is defined by
f: (x,y)--> (x + y, x - y). Find
a) f(2,0).
b) f(-1,-2).
Ratio and proportion
) In a mixture of 45 litre, the ratio of milk and water is 4:1. How much water must be added to make the ratio 3:2 ?
) If b is the mean proportional between a and c, prove that: (a²- b²+ c²)/(a⁻² - b⁻² + c⁻²) = b⁴.
) If (ay - bx)/p = (CX - az)/q = (bz - cy)/r, show that x/a = y/b = z/c.
) If x= {√(2a+1) + √(2a -1)}/{√(2a +1) - √(2a -1)}, show that x² - 4ax +1=0.
) If (3x +4y)/((3u +4v) = (3x -4y)/(3u - 4v), show that x/y = u/v.
Metrices
) If B= 2 -3 and C= 1 -3
-4 5 -4 4 find the matrix B - C.
) If A= a 3 B= 2 b C= 1 1 D= 5 0
4 2 1 -2 -2 c 7 3 with the relation A + B - C = D, then find a, b and c.
) If M= 2 0 and N= 2 0
1 2 -1 2 , find M + 2N.
) If A= 4 -2 B= 0 2 and C= -2 3
6 -3 1 -1 1 -3 find A² - A + BC.
) If A= 3 4 B= a b C= 1 0
2 5 c d 0 1 with the relation A= BC then find the value of a, b and c.
) If A= 2 x & B= 4 36
0 1 0 1 find the value of x, given that A²= B.
) If A= p q & B= p & C= 25
q
with the relation AB= C, then find p, q.
) If A= 1 2 B= x 0 & C= x 0
3 3 0 y 9 0 find the values of x and y, given AB = C.
) If A= 2 3 B= x & C= 7
-1 0 y -2 find the value of x and y, given AB = C.
) Given A= 3 0 & B= a b
0 4 0 c and that AB= A+ B, find the values of a, b and c.
) If A= x -2 5 B= 4 2 & C= -4 3
3 3 y 5 -1 -2 Find x and y, given A= B + C.
) If A= 1 2 B= 2 1 & C= 1 3
2 3 3 2 3 1 find C(B - A)
Distance and Section formulas
) Point A and B have co-ordinates (3,5),( x, y) respectively. The mid point of AB is (2,3). Find the values of x and y.
) Calculate the coordinates of the point P which divides the line joining A(1,3),(5,9) in the ratio 1:2.
) Given 3x + 2x + 4 =0
a) Express the equation in the form y= mx+ c.
b) Find the slope and the y- intercept of the line 3x + 2y + 4 = 0.
c) use your answer (b) above and on a graph paper draw the graph of the straight line 3x + 2y +4=0.
) The graph of the equation y= mx+ c passes through the points (1,4) and (-2,-5). Determine the values of m and c.
) the line represted by 3x+ 4y =8 and px + 2y =7 are parallel. Find the value of p.
) The coordinates of two points E and F are (0,4) and (3,7) respectively. Find
a) the gradient of EF.
b) the equation EF.
c) the co-ordinates of the point where the line EF intersect the x-axis.
) P,Q, R have co-ordinates (-2,1),(2,2) and (6,-2) respectively. Write down
a) the gradient of QR.
b) the equation of the line through P P perpendicular to QR.
) Find the equation of the line parallel to X - 2y +8=0 and passing through the point (1,2).
) The distance between A(1,3) and B(x, 7) is 5. Calculate the possible of x.
) Given that the co-ordinates of the points A and B are (-3,2) and (9,7) respectively. find
a) the co-ordinates of midpoints of AB
b) the distance between A and B.
) The coordinates of two points A and B are (-3,3) and (12,- 7) respectively. P is a point on the line segment AB such that AP:PB = 2:3. Find the coordinates of P without using squared paper.
) Find the slop of a line joining the point (3,4) and (0,16). Hence or otherwise, write down the equation of this line.
) The equation of a line is y = 3x -5. Write down the slope of this line and the intercept made by it on the y-axis. Hence or otherwise, write down the equation of a line which is parallel to this line and which passes through the point (0,5).
) Find the value of p if the lines , whose equations are y=3 x +7 and 2y+ px= 3 are perpendicular to each other.
) Find the co-ordinates of the point of intersection of the line represented by by x + y= 6, 3x - y = 2.
) B, C have coordinates (3,2),(0,3). Find
a) the image B' of B under the reflection in the x-axis,
b) the image C' of C under reflection in the line BB',
c) calculate the length of B'C.
) The image of a point P under reflection in the x-axis is (5,-2). Write down the co-ordinates of P.
) A point P is reflected in the x-axis. Coordinate of its image are (8,-6)
a) find the coordinates of P.
b) Find the coordinates of the image of P under reflection in the y-axis.
) The triangle ABC where A(1,2), B(4,8), C(6,8) is reflected in the x-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to trianglebA''B''C''. Write down the co-ordinates of A",B",C". Write down the single transformation that maps ABC into A''B''C''.
Geometry
) In the figure given, sides QT and RS of the cyclic quadrilateral RQST are produced to meet at P. Given that angle ROT= TSR =90°, QR= 10cm, PQ =24cm, find PR .
it is further given that PS/SR =3/10, find PS and ST. 26,6,2.5
) Prove that parallelograms on the same base and between the same parallels are equal in area.
) The internal bisectors of the angle B and C of a triangle ABC meet at I. Given that angle A=60°, find the numerical value of angle BIC. 120°
) ABCD is a quadrilateral inscribed in a circle on AC as a diameter. AB and DC produced meet takes at X, BC and AD produced meet at Y. Prove that YDBX is a cyclic quadrilateral.
) In the figure, AC is a transverse common tangent to two circles with centre P and Q and radius 6cm and 3cm respectively. Given that AB =8cm, calculate PQ. 15cm
) ABCD is ||GM; any line through A cuts DC at point P and BC produced at Q. Prove that ∆ BCP is equal in area to ∆DPQ.
) In the given figure, P and Q are the centres of two circles intersecting at B and C. ACD is a straight line. Calculate the numerical value of x. 130°
) Prove that equal chords equaidistant from the centre of a circle.
) PQRS is a trapezium in which PQ is parallel to SR. PR and QS intersect at T. PR=7cm, SR =10.5 cm. If the area of PQT=20 cm², find the area of
a) ∆ STR . 45cm²
b) ∆ QTR. 30cm²
) The diagonals of a parallelogram ABCD, intersect in E. Through E, a line is drawn parallel to BC , to meet AB in X and CD in Y. prove that
a) X and Y are mid point of AB and CD respectively.
b) area ∆BCE =1/4 area of a parallelogram ABCD.
) In the given figure O is the centre of the circle, PS and PT are tangents and angle SPT=84°. Calculate the sizes of the angles tof TOS , TQS. 96°,132°
) In the given figure EF is parallel to BC and EF: BC = 3:5.
Calculate the ratio of the areas of the triangle AEF and trapezium EFCB . 9:16
) in the given figure angle ABC is a right angle, M is the midpoint of AC, AB =12cm and BC =5cm. Calculate the length of the BM. 6.5cm
) In the given figure AB= BC and AD is perpendicular to CD. Prove that AC ²= 2. BC. CD.
) AX and DY are the altitude of two similar triangles ABC and DEF. Prove that prove AX: DY = AB : DE.
) Prove that the tangent drawn to a circle from an external point are equal.
) In the given figure QPX is the bisector of the angle XYZ of the triangle XYZ. Prove that: XY: XQ = XP: XZ.
) In the given figure ED and BC are two parallel chords of the circle and AbE and ACD are two straight lines. Prove that AED is an isosceles triangle.
) In figure , the diagonals AC and BD of a quadrilateral ABCD intersect in O, at right angles.
Prove that AB²+ CD²= AD²+ BC².
) in the given figure O is the centre of the circle.
angle AOE= 150°, angle DAO =51°.
Calculate the sizes of the angles CEB and CBE. 51,105
) in the given figure D is parallel to BC and the ratio of the area of the triangle A D E and trapezium BTech is 4:5 find the ratio bebc in the given figure aedc 13 be 5 ABC 90 and 80 X calculate the length of a b and the value of x o is any point inside a rectangle prove that the medians of two similars prove that prove that the opposite angle of a cyclic quadrilateral are supplementary in the given figure x y z is a triangle inscribed in a circle XN is the altitude of the triangle of the circle prove that in the given figure SP is the bisector of rpt and pqrs in the cyclic quadrilateral prove that x q SR in the figure x and y are the midpoint of ab and ac respectively given that BC 6 ab 5.4 AC 5.0 CM calculate the perimeter of the trapezium xy CB the figure represent to triangle ABC and pqr in which ACB pqr 50 BSc QPR 68 ABC pqr 70 abpq X side AC 5 PR 3.2 calculate the side ab in the figure it is given that ABC 48 is a diameter of the circle calculate DC the figure shows to circles is intercept at A and B the centre of the smaller circle is over analyse on the circumference of the largest given 75 calculate the value of ab Tuesday OB ADB giving clear reason for your answer in the given figure pqr is a right angle triangle in the given figure ab just side up a regular 5 sided polygon and ac the side of a regular six sided polygon inscribed in a circle centre is calculated the sizes of Asda CD ABC in figure triangle ABC is a right angle at B given that AB 9 AC 15 and D E are the mid points of the side ab and ac respectively calculate the length of BC the area of the triangle ABC centre of the triangle ABC which AC BC given that angle ACB 56 calculate angle cave angle AC in the diagram eyes the incense of the triangle x y z x i produced with the circumcircle of the triangle x y z w angle y x z50 angle XZ Y 70 calculate angle wyz angle yiw in the adjoining figure ABCDE and EA per parallel lines given that AB 6D Y year 10 AC 4 and cfx calculate the value of x and y in a triangle calculate the length of a direct common tangent to a two circle of radi38 with their centres 13 cm apart in the adjoining figure pqrprs prove that triangle pqr TRS are similar pr8 PS4 calculate pk in the joining figure ad year medians of triangle abcdef is drawn parallel to be EF CAG is to GD 2:1 in the adjoining figure prove that prove that angles in the same segment of a circle are equal in the adjoining figure ab is a diameter of the circle centre ODIs parallel to BC and angle aod 60 calculate the numerical value of angle ABT angle d b c angle ADC in the evening is a point on a b c such that be 5A produced in a DC produced at F calculate the length of a prove that the triangle ABC is similar to Triangle fce le the length of year and CA in the triangle ABC ABC X CM BC 10 cm area the triangle 60 write down the equation and X and salt with two part time x the side of a b d c of a cyclic quadrilateral ABCD as produced to meet at P the sides a d and the BC are produced to metre cube angle a DC 85 the angle BTC 40 calculate the angle B and angle cq d the ready of the two concentric circles are 17 10 lines pqrs larger circle at pns and the smaller circle two circle touch each other the point of contact lies on the straight line through their centres prove that use in the triangle abcdees the mid point of BC and a d is perpendicular to BC prove that ad is the line of symmetry of triangle in the lungside B.Ed c a e a d b prove that ABC similar in the figure given a long side is the midpoint of AC and if is perpendicular to acax bisect BSE MITS DC at d and d e at Y prove that a point Y is equal distance from a and c point D = distance from a and c in the figure alongside with the centre of the circle XO why 40 twx 120 and xy parallel to TZ point XZ yxzx
1) tanx=4/3, find without using tables ,the value of sinx + cosx(both sinx and cosx are positive). 1.4
2) Given sinx= p/q, find in terms of p and q, cosx + tanx. √(q²- p²)/q + p/(q²- p²).
3) Given tanA=3/4 that find the value of
a) sinA. 3/5
b) cosA. (A is an acute angle). 4/5
4) In the adjoining figure,
a) tan x°. 6/5
b) sin y°. 5/13
c) cos y°. 12/13
5) Using the measurements given in the figure.
b) Write an expression for AD in terms of θ. 9/cos θ or 12/sinθ
6) In the triangle given alongside, find θ,
7) Find the value of (sin² 45 +cos² 45)/tan²60. 1/3
8) find the value of (sin² 30+ cos² 45+ sin² 60)/ Tan2 30. 9/4
9) Evaluate : cos 90°+ cos² 45 sin 30° tan45°. 1/4
10) Evaluate : 4/3 tan²30°+ sin²30° - 3 cos² 60° +3/4 tan² 60° - 2 tan²45. 25/36
11) If 4 sin² θ -1=0 and angle θ is less than 90°, find the value of θ and hence the value of cos²θ+ tan²θ. 30°, 13/12
12) if x= 30°, verify, tan2x= 2tanx/(1- tan²x).
13) if 0≤ x ≤90°, state the numerical value of x for which sin x°= cos x°. 45°
14) ABC is a right angled triangle, right angled B.
15) If the length of a shadow cast by a pole be √3 times the length of the pole, find the angle of elevation of the Sun. 30°
16) In the given figure:
a) AD. 35.32cm
b) the perpendicular distance between BC and AD. 5cm
17) The shadow of a tower on level ground increases in length by x metres when the altitude of the sun changes from 45° to 30°. Calculate the value of x, given that the height of the tower is 25 m. 18.3cm
18) AD is drawn perpendicular to BC, the base of an equilateral triangle ABC. Given BC=10cm, find the length of AD correct to 1 place of decimals. 8.7cm
19) From a light house the angles of depression of two ships on opposite sides of the light house were observed to be 30° and 45°. If the height of the lighthouse is 90 m and the line joining the two ships passes through the foot of the light house , find the distance between the two ships . Give your answer correct to 2 decimal places. 245.88 m
20) An observer standing in 60m away from a building notices that the angles of elevation of the top and the bottom of a flag-staff on the building are respectively 60° and 45°. Find the height of the flG-staff. 43.92
21) Two men are on the opposite sides of a tower. They measue the angle of elevation of the top of tower as 45° and 30° respectively. If the height of the tower is 40m find the distance between the men. 109.28
22) The shadow of a tower, when the angle of elevation of the sun is 45°, is found to be 10m longer than when it is 60°. Find the height of the tower. 23.66m
23) A ladder of length of 4 m makes an angle of 30° with the floor while leaning against the wall of a room. If the foot of the ladder is kept fixed on the floor and it is made to lean against the opposite wall of the room, it makes an angle of 60° with the floor. Find the distance between these two walls of the room. 5.464m
24) Two men are on the opposites sides of a tower. they measure the angles of elevation of the top of the tower 45° and 60° respectively. if the height of the tower is 40 m, find the distance between the men. 63.09m
25) The angle of elevation of the top of the tower from a point on the ground is found to be 45°. By going 50 m further away from the tower, it is found to be 30°. Find the height of the tower. 68.3
26) From the top of a building 60 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60°. Find the height of the tower. 40cm
27) Two vertical poles are fixed 60m apart. The angle of depression of the top of the first as seen from the top of the second, which is 150m high is 30°. Find the height of the first pole. 120m
28) An artist climbs a rope stretched from the top of a pole and fixed on the ground. The height of the pole is 10 m and the angle made by the rope with the ground is 30°. Find the length of the rope. 20m
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