
question_answer1) From a distance of 100 m from the foot of a building, the angle of elevation of its top is \[\text{3}0{}^\circ \]. What is the height of the building?
A) \[57.7\,m\]
B) \[100\sqrt{3}\,m\]
C) \[5.77\,m\]
D) \[\frac{100}{3}\,m\]
View Answer play_arrow

question_answer2) The angles of elevation of the top from two points on either side of a tree are\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \]. What is the height of the tree if the two points are 52 m apart?
A) 39 m
B) 22.5 m
C) 65 m
D) 225 m
View Answer play_arrow

question_answer3) The angle of depression of a car from the top of a 20 m high tower is\[\text{6}0{}^\circ \]. At what distance from the foot of the tower is the car?
A) 16m
B) 8m
C) 22m
D) 12m
View Answer play_arrow

question_answer4) The height of a kite from the ground is 100 Vim. If the angle of elevation from a point on the ground is\[\text{45}{}^\circ \], what is the length of the string of the kite?
A) \[100\sqrt{3}\,m\]
B) \[100\sqrt{2}\,m\]
C) \[100\sqrt{6}\,m\]
D) 100 m
View Answer play_arrow

question_answer5) A 24 m tall tree was cut to a height from the ground. The top of the tree touching the ground makes an angle\[\text{3}0{}^\circ \]with the ground. At what height from the ground was the tree cut?
A) 4 m
B) 8 m
C) 10 m
D) 6 m
View Answer play_arrow

question_answer6) A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is\[\text{3}0{}^\circ \]. He moves 40 m towards the bank and finds the angle of elevation to be\[\text{6}0{}^\circ \]. What is the width of the river?
A) 24 m
B) 20 m
C) 26 m
D) 15 m
View Answer play_arrow

question_answer7) The angles of elevation of the sun changes from\[\text{45}{}^\circ \]to\[\text{3}0{}^\circ \].Then the shadow of a tower on the ground increases by 10 m. What is the height of the tower?
A) 13.65m
B) 13.56m
C) 15.63m
D) 15.36m
View Answer play_arrow

question_answer8) From an aero plane at an altitude of 900 m, two cars moving towards it in the same direction are found to be\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the distance between the cars?
A) 415m
B) 315.4m
C) 380.4 m
D) 305 m
View Answer play_arrow

question_answer9) From a tower of 200 m, the angles of depression of two buildings in opposite sides of the tower are found to be\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the distance between the buildings?
A) 415m
B) 315.4m
C) 200 m
D) 305 m
View Answer play_arrow

question_answer10) The angles of elevation of the top of a building from the ground floor and first floor of another building are\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \] respectively. If the first floor is 40 m above the ground floor, what is the height of the building?
A) 54.64m
B) 94.64m
C) 40m
D) 109.3m
View Answer play_arrow

question_answer11) From two opposite ends of a 100 m wide road, the angles of elevation of the top of a clock tower are found to be\[\text{3}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the height of the clock tower?
A) 36.6 m
B) 36 m
C) 37 m
D) 35.4 m
View Answer play_arrow

question_answer12) Two buildings are 140 m apart. The angle of elevation of the top of a building as seen from the top of the other is\[\text{3}0{}^\circ \]. If the second building is 60 m tall, how tall is the first building?
A) 83 m
B) 80.83
C) 84m
D) 140.83
View Answer play_arrow

question_answer13) What is the angle of elevation of a light source when the length of the shadow of a flag post is equal to its height?
A) \[\text{45}{}^\circ \]
B) \[\text{3}0{}^\circ \]
C) \[\text{6}0{}^\circ \]
D) (d)\[\text{9}0{}^\circ \]
View Answer play_arrow

question_answer14) A ladder 19 m long is placed leaning against a wall. If the angle of elevation of the ladder is\[\text{6}0{}^\circ \], how far is the ladder from the wall?
A) 11 m
B) 9.5 m
C) 10.5 m
D) 9 m
View Answer play_arrow

question_answer15) A gas balloon is tied with a 215 m long rope with an inclination of\[\text{45}{}^\circ \]with the horizontal. How high is the balloon?
A) 166m
B) 178m
C) 152m
D) 184m
View Answer play_arrow

question_answer16) From a 50 m tall building, the angles of depression of the top and foot of a temple are found to be 30? and 60? respectively. What is the height of the temple?
A) 36m
B) 25.3m
C) 33.33m
D) 30m
View Answer play_arrow

question_answer17) The angle of elevation of a flag on a school building is\[~\text{45}{}^\circ \]. Moving 40 m towards the building, the angle of elevation is found to be\[\text{6}0{}^\circ \]. What is the height of the flag from the ground?
A) 40 m
B) 94.64 m
C) 60 m
D) 54.64 m
View Answer play_arrow

question_answer18) The angle of elevation of the top of a 'Br tower from the foot of a hillock is\[\text{6}0{}^\circ \]. The angle of elevation of the top of the hillock from the foot of the tower is\[\text{3}0{}^\circ \]. If the hillock is 50 m, what is the height of the tower?
A) 50m
B) 140m
C) 100m
D) 150m
View Answer play_arrow

question_answer19) From a 200 m tall tower, the angles of depression of the top and bottom of a pole are\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \]respectively. What are the respective values of height and distance of the pole from the tower?
A) 133.33m, 115.46m
B) 115.46m, 133.33m
C) 115.33 m, 66.33m
D) 145.46m.33m
View Answer play_arrow

question_answer20) The string of a kite is 200m long. It makes an angle of\[\text{3}0{}^\circ \]with the ground. What is the height of the kite above the ground?
A) 120m
B) 150m
C) 100m
D) 200m
View Answer play_arrow

question_answer21) An eagle flying at an altitude of 1200 m flies vertically above another eagle at the same time, when the angles of elevation of the two birds are\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \] respectively. How high above the second eagle is the first eagle flying?
A) 507.20 m
B) 500 m
C) 570.81 m
D) 300 m
View Answer play_arrow

question_answer22) A 15 m long ladder placed vertically along a wall broke in such a way that its top touches the ground making an angle of\[\text{6}0{}^\circ \]with it. At what height from the ground did the ladder break?
A) 7.34m
B) 8m
C) 9.46 m
D) 6.96 m
View Answer play_arrow

question_answer23) From a window A, 10 m above the ground, the angle of elevation of the top C of a tower is \[\text{x}{}^\circ \], where \[\tan x{}^\circ =\frac{5}{2}\], and the angle of depression of the foot D of the tower is \[\text{y}{}^\circ \], where tan \[\text{tan}\,\text{y}{}^\circ =\frac{1}{4}\]. What is the height CD of the tower to the nearest metre?
A) 135m
B) 75m
C) 59m
D) 110m
View Answer play_arrow

question_answer24) PQ is a tower standing on a horizontal plane, Q being the foot of the tower. A and B are two points on the plane such that\[\angle \text{BQP}\] is\[\text{9}0{}^\circ \], AB = 4 m. If \[\cot (\angle PAQ)=\frac{3}{10}\]and\[\cot (\angle PBQ)=\frac{1}{2}\], find the height of the tower.
A) 10m
B) 15m
C) 18m
D) 20m
View Answer play_arrow

question_answer25) The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angles of elevation of the tops of the poles from the middle point of the line segment joining their feet are complementary to each other. Find the heights of the poles.
A) 21.21 m, 42.42m
B) 36.63 m, 67.76 m
C) 42.24m.10.01 m
D) 16.16m, 22.22m
View Answer play_arrow

question_answer26) The shadow of a person X, when the angle of elevation of the sun is a, is equal in length to the shadow of person Y, when angle of elevation of the sun is\[\left( \frac{\alpha }{2} \right)\]. Which one of the following is correct?
A) X is shorter than Y.
B) X is twice as tall as Y.
C) X is taller than Y but is not twice as tall as Y.
D) Both X and Y are of equal of height.
View Answer play_arrow

question_answer27) Two observers are stationed north of a tower at a distance of 20 m from each other. If the elevation of the tower observed by them are \[\text{3}0{}^\circ \]and\[\text{45}{}^\circ \], respectively, find the height of the tower.
A) 10m
B) 16.32m
C) \[10(\sqrt{3}+1)m\]
D) 30m
View Answer play_arrow

question_answer28) If the angle of depression and elevation of the top of a tower of height 'h' from the top and bottom of a second tower are x and y respectively, find the height of the second tower.
A) \[h(\cot y\cot x)\]
B) \[h(\tan x+\tan y)\]
C) \[h(1+\tan x\cot y)\]
D) \[h(\tan y.\cot x+1)\]
View Answer play_arrow

question_answer29) Two posts are 25m and 15m high and the line joining their tops makes an angle of\[\text{45}{}^\circ \]with the horizontal. What is the distance between these posts?
A) 5 m
B) \[\frac{10}{\sqrt{2}}m\]
C) 10m
D) \[10\sqrt{2}\,m\]
View Answer play_arrow

question_answer30) The angle of elevation of the top of an incomplete tower at a point 40 m from its base is\[\text{45}{}^\circ \]. If the elevation of the completed tower at the same point is\[\text{6}0{}^\circ \], find the height through which the tower has been raised.
A) \[40\sqrt{3}m\]
B) \[40(\sqrt{3}+1)m\]
C) \[40\left( 1\frac{1}{\sqrt{3}} \right)m\]
D) \[40(\sqrt{3}1)m\]
View Answer play_arrow

question_answer31) The angle of elevation of an object from a point 500 m above a lake is observed to be \[\text{3}0{}^\circ \] and the angle of depression of its reflection in the lake is\[~\text{45}{}^\circ \]. Find the height of the object above the lake.
A) \[\frac{500}{\sqrt{3}}(1+\sqrt{3})m\]
B) \[500(2+\sqrt{3})m\]
C) \[500(3+\sqrt{3})m\]
D) \[500(4+\sqrt{3})m\]
View Answer play_arrow

question_answer32) A flag  staff is fixed at the top of a tower. The angles of elevation of the top and the bottom of this flagstaff at a point distant 'a' m from the foot of the tower, are\[\alpha \]and\[\beta \], respectively. Find the height of the flag staff (in m).
A) \[a(\sin \alpha \sin \beta )\]
B) \[a(\cos \beta \cos \alpha )\]
C) \[a(\tan \alpha \tan \beta )\]
D) \[a\tan (\alpha \beta )\]
View Answer play_arrow

question_answer33) The height of a tower is h m and the angle of elevation of the top of the tower is a. On moving a distance h/2 towards the tower, the angle of elevation becomes P. What is the value of\[\cot \alpha \cot \beta \]?
A) \[\frac{1}{2}\]
B) \[\frac{2}{3}\]
C) 1
D) 2
View Answer play_arrow

question_answer34) From the top of a 60 m high tower, the angle of depression of the top and bottom of a building are observed to be\[\text{3}0{}^\circ \]and\[\text{6}0{}^\circ \] respectively. Find the height of the building.
A) \[60\sqrt{3}\,m\]
B) \[40\sqrt{3}\,m\]
C) 40 m
D) 20 m
View Answer play_arrow

question_answer35) A landmark on the bank of a river is observed from two points X and Y on the opposite banks of the river. The lines of sight make equal angles with the bank of the river. If XY = 1 km, what is the width of the river?
A) \[\frac{3}{2}km\]
B) \[\frac{1}{2}km\]
C) \[\frac{3\sqrt{2}}{2}km\]
D) \[\frac{3\sqrt{3}}{2}km\]
View Answer play_arrow

question_answer36) A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is\[\text{45}{}^\circ \]. Which of the following is true?
A) Breadth of the river is twice the height of the tower.
B) Height of the river is twice the breadth of the river.
C) The height of the tower and the breadth of the river are equal.
D) Breadth of river is thrice the height of the tower.
View Answer play_arrow

question_answer37) The angles of elevation of the top of a vertical tower from points at distance a and b from the base and in the same line with it are complementary. If a > b, find the height of the tower.
A) \[\sqrt{ab}\]
B) \[\sqrt{(a+b)}\]
C) \[\sqrt{(a/b)}\]
D) \[\sqrt{(ba)}\]
View Answer play_arrow

question_answer38) A tower subtends an angle of\[~\text{3}0{}^\circ \]at a point on the same level as the foot of the tower. At a second point h m above the first, the depression of the foot of the tower is 60?. What is the horizontal distance of the tower from the point?
A) \[\text{h cot 6}0{}^\circ \]
B) \[\text{h cot 3}0{}^\circ \]
C) \[\frac{h}{2}\text{cot 6}0{}^\circ \]
D) \[\frac{h}{2}\text{cot 3}0{}^\circ \]
View Answer play_arrow

question_answer39) Starting from the same point in a leveled field, Rahul walked 1000 m due East and then 1000 m due North whereas Aryan walked 2000 m NorthEast. At the end of the walks, what is the distance between Rahul and Aryan?
A) Zero
B) 828 m
C) 586m
D) 1000m
View Answer play_arrow

question_answer40) If a flag staff of 6 m height placed on the top of a tower throws a shadow of \[2\sqrt{3}m\]along the ground, find the angle that the sun makes with the ground.
A) \[\text{6}0{}^\circ \]
B) \[\text{3}0{}^\circ \]
C) \[\text{45}{}^\circ \]
D) \[~\text{9}0{}^\circ \]
View Answer play_arrow

question_answer41) The angle of elevation of a jetfighter from a point P on the ground is\[\text{6}0{}^\circ \]. After five seconds of flight, the angle of elevation changes to\[\text{45}{}^\circ \]. If the jet is flying at a height of 3000 m. find the speed of the jet, in m/s.
A) \[1000(3\sqrt{3})\]
B) \[200(3\sqrt{3})\]
C) \[1000\sqrt{3}\]
D) \[600\]
View Answer play_arrow

question_answer42) The angles of elevation of the tops of two pillars of height h and 2h from a point on the line joining the feet of the two pillars are complementary. lf the distances of the feet of the pillars from that point are x and y respectively, find the value of 2h2.
A) \[{{x}^{2}}y\]
B) \[x{{y}^{2}}\]
C) \[xy\]
D) \[{{x}^{2}}{{y}^{2}}\]
View Answer play_arrow

question_answer43) A round balloon of radius 'r' subtends an angle\[\alpha \]at the eye of an observer, while the angle of elevation of its centre is\[\beta \]. Find the height of the centre of the balloon.
A) \[r\sin \frac{\alpha }{2}\cos ec\beta \]
B) \[r\cos ec\frac{\alpha }{2}\cos \beta \]
C) \[r\cos \frac{\alpha }{2}\cos ec\beta \]
D) \[r\cos ec\frac{\alpha }{2}\sin \beta \]
View Answer play_arrow