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 30° and the angle of depression of the image of the aeroplane in the water of the lake is 60°. 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 30° and 60°. 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 60° and the angle of depression of the foot of the tower is θ. Such that tan θ = $$\frac{3}{4}$$, what is the height of the tower (√3 = 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 sun’s elevation is 30° than when it was 45 °. 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 30° and the angle of depression of its reflection in the lake is 60°. 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 45° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60° 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 60° and 30°, respectively and the distance between them is 84√3 m. What is the height (in m) of the pole?

  • (A) 60
  • (B) 63
  • (C) 52.5
  • (D) 73.5