Height & Distance Mcqs - Set 1

1)   The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole ?

a. 5 metres
b. 8 metres
c. 10 metres
d. 12 metres
Answer  Explanation 

ANSWER: 10 metres

Explanation:
No explanation is available for this question!

2)   The angle of elevation of the sun, when the length of the shadow of a tree is √3 times the height of the tree, is :________?

a. 30°
b. 45°
c. 60°
d. 90°
Answer  Explanation 

ANSWER: 30°

Explanation:
No explanation is available for this question!

3)   From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is :_________?

a. 149 m
b. 156 m
c. 173 m
d. 200 m
Answer  Explanation 

ANSWER: 173 m

Explanation:
Let AB be the tower. Then, ∠APB = 30° and AB = 100 m, AB/AP = tan 30° = 1/√3 AP = (AB X √3)= 100√3 m. = (100 X 1.73) m = 173 m.

4)   If the height of a pole is 2√3 metres and the length of its shadow is 2 metres, find the angle of elevation of the sun.

a. 50°
b. 60°
c. 70°
d. 80°
Answer  Explanation 

ANSWER: 60°

Explanation:
Let AB be the pole and AC be its shadow. Let angle of elevation, ∠ACB = θ. Then, AB = 2√3m, AC = 2 m. tan θ = AB/AC = 2√3/2 = √3 θ = 60°. So,the angle of elevation is 60°

5)   Two ships are sailing in the sea on the two sides of a lighthouse. The angles of elevation of the top of the lighthouse as observed from the two ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is :_________?

a. 173 m
b. 200 m
c. 273 m
d. 300 m
Answer  Explanation 

ANSWER: 273 m

Explanation:
Let AB be the lighthouse and C and D be the
positions of the ships. Then,
AB = 100 m, ∠ACB = 300 and ∠ADB = 45°.
AB/AC = tan 30° = 1/√3
AC = AB X √3 = 100√3 m.
AB/AD = tan 45° = 1 ⇒ AD = AB = 100 m.
CD = (AC + AD) = (100√3 + 100) m
= 100 (√3 +1) m = (100 X 2.73) m = 273 m.

6)   The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is :_________?

a. 2.3 m
b. 4.6 m
c. 7.8 m
d. 9.2 m
Answer  Explanation 

ANSWER: 9.2 m

Explanation:
Let AB be the wall and BC be the ladder. Then, ∠ACB = 60° and AC = 4.6 m. AC/BC = Cos 60° = 1/2 BC = 2 X AC = (2 X 4.6) m = 9.2 m.

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