Question

Two men are on opposite side of tower. They measure the angles of elevation of the top of the tower as 30° and 45° respectively. If the height of the tower is 50 meters, find the distance between the two men.

Answer 1

Let CD be the tower and A and B be the positions of the two men standing on the opposite sides.

Thus, we have:

∠DAC = 30°, ∠DBC = 45° and CD = 50 m

Let AB = x m and BC = y m such that AC = (x - y)m.

In the right △DBC, we have:

On putting y = 50 in the above equation, we get: