Question

A tower subtends an angle of 30 at a point on the same level as its foot, and at a second point h m above the first, the depression of the foot of tower is 60 . The height of the tower is

(A) h m

(B) 3h m

(C) √3 h m

(D) h3 m.

Answer 1

Correct Answer is: (D) h3 m.

Let OP be the tower of height x., A the point on the same level as the foot O of the tower and B be the point h m above A (see Fig.). Then ∠ AOB = 60 and ∠ PAO = 30 .

From right-angled triangle AOP, we have OA = x cot 30 and from right-angled triangle OAB, we have OA = h cot 60

Therefore, from (1) and (2), we get

x cot 30 = h cot 60