100+ Heights and Distance Aptitude Questions and Answers - 1

Question: 1

On the same side of a tower, two objects are located. Observed from the top of the tower, their angles of depression are 45° and 60°. If the height of the tower is 150 m, the distance between the objects is

(A) 53.5 m

(B) 63.5 m

(C) 76.9 m

(D) 86.7 m

Ans: B

Question: 2

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) 240 m

(D) 273 m

Ans: D

Question: 3

If a 30 m ladder is placed against 1 15 m wall such that it just reaches the top of the wall, then the elevation of the wall is equal to

(A) 30°

(B) 45°

(C) 50°

(D) 60°

Ans: A

Question: 4

A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30° with the man’s eye. The man walks some distance towards the tower to watch its top and the angle of elevation becomes 60°. What is the distance between the base of the tower and the point P?

(A) 4 units

(B) 8 units

(C) 12 units

(D) Data inadequate

Ans: D

Question: 5

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) 20°

(B) 30°

(C) 40°

(D) 50°

Ans: B

Let AB be the tree and AC be its shadow.

Let ∠ACB = Θ.

Then, $${AC}/ {AB}$$ = &radic3;

⇒ cot θ = &radic3; ⇒ = θ = 30°