Practice MCQ Questions and Answer on Height and Distance
1.
The angle of elevation of an aeroplane as observed from a point 30 m above the transport water-surface of lake is 30ÃÂÃÂÃÂð and the angle of depression of the image of the aeroplane in the water of the lake is 60ÃÂÃÂÃÂð. The height of the aeroplane from the water-surface of the lake is
- (A) 60 m
- (B) 45 m
- (C) 50 m
- (D) 55 m
2.
From the top of a hill 200 m high the angle of depression of the top and the bottom of a tower are observed to be 30ÃÂÃÂÃÂð and 60ÃÂÃÂÃÂð. The height of the tower is (in m);
- (A) $$\frac{{400\sqrt 3 }}{3}$$
- (B) $$166\frac{2}{3}$$
- (C) $$133\frac{1}{3}$$
- (D) $$200\sqrt 3 $$
3.
Due to sun, a 6ft man casts a shadow of 4ft, whereas a pole next to the man casts a shadow of 36ft. What is the height of the pole?
- (A) 63 ft
- (B) 72 ft
- (C) 54 ft
- (D) 48 ft
4.
From the top of a 12 m high building, The angle of elevation of the top of a tower is 60ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð and the angle of depression of the foot of the tower is ÃÂÃÂÃÂÃÂÃÂÃÂÃÂø. Such that tan ÃÂÃÂÃÂÃÂÃÂÃÂÃÂø = $$\frac{3}{4}$$, what is the height of the tower (ÃÂÃÂÃÂâÃÂÃÂÃÂÃÂ3 = 1.73)?
- (A) 39.68 m
- (B) 41.41 m
- (C) 37.95 m
- (D) 36.22 m
5.
The length of the shadow of a tower standing on level ground is found to 2x meter longer when the sunÃÂÃÂÃÂâÃÂÃÂÃÂÃÂs elevation is 30ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð than when it was 45 ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð. The height of the tower in meters is
- (A) $$\left( {\sqrt 3 + 1} \right)\,x$$
- (B) $$\left( {\sqrt 3 - 1} \right)\,x$$
- (C) $$2\sqrt 3 \,x$$
- (D) $$3\sqrt 2 \,x$$
6.
Find the angle of elevation of the sun when the shadow of a pole of 18 m height is $$6\sqrt 3 $$ m long?
- (A) 30°
- (B) 60°
- (C) 45°
- (D) None of these
7.
The angle of elevation of a cloud from a point 200 m above a lake is 30ÃÂÃÂÃÂð and the angle of depression of its reflection in the lake is 60ÃÂÃÂÃÂð. The height of the cloud is-
- (A) 200 m
- (B) 300 m
- (C) 400 m
- (D) 600 m
8.
Rohit while seeing a bird on tree top made 45ÃÂÃÂÃÂð angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60ÃÂÃÂÃÂð angle of elevation. How far was Rohit from the tree initially?
- (A) $$\frac{{240\sqrt 3 }}{{\sqrt 3 - 1}}\,{\text{ft}}$$
- (B) $$\frac{{240}}{{\sqrt 3 - 1}}\,{\text{ft}}$$
- (C) $$\frac{{240}}{{\sqrt 3 }}\,{\text{ft}}$$
- (D) $$240\sqrt 3 \,{\text{ft}}$$
9.
A person was standing on a road near a mall. He was 1215 m away from the mall and able to see the top of the mall from the road in such a ways that the top of a tree, which is in between him and the mall, was exactly in line of sight with the top of the mall. The tree height is 20 m and it is 60 m away from him. How tall (in m) is the mall?
- (A) 375
- (B) 300
- (C) 405
- (D) 250
10.
P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are 60ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð and 30ÃÂÃÂÃÂÃÂÃÂÃÂÃÂð, respectively and the distance between them is 84ÃÂÃÂÃÂâÃÂÃÂÃÂÃÂ3 m. What is the height (in m) of the pole?
- (A) 60
- (B) 63
- (C) 52.5
- (D) 73.5