Calculate the distance between the vehicles.

From the top of a church spire 96 m high, the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y°, where tan x° = and tan y° = . Calculate the distance between the vehicles. (1994)

Solution:

Height of the church CH.
Let A and B are two vehicles which make the angle of depression
from C are x° and y° respectively.

In the adjoining figure, not drawn to the scale, AB is a tower and two objects C and D are located on the ground, on the same side of AB. When observed from the top A of the tower, their angles of depression are 45° and 60°. Find the distance between the two objects. If the height of the tower is 300 m. Give your answer to the nearest metre. (1998)

Solution:

Let CB = x and
DB = y
AB = 300 m

More Solutions:

• Solve the following trigonometric:
• Evaluate trigonometric:
• Solve trigonometric:
• Solve: (1 + tan A)/sin A + (1 + cot A)/cos A = 2(sec A + cosec A)
• Prove the identity:
• Solve: (sinθ + cosθ)(secθ + cosecθ) = 2 + secθ cosecθ.