Question

4) The hospital and the fire department are 46 meters apart. From a window in the hospital,

the angle of elevation to the top of the fire department is 730. From the same window, the
angle of depression to the ground at the base of the fire department is 640. Find the height
of the fire department to the nearest tenth.

Answer 1

The height of the fire department is 244.72 m

Explanation:

A)

Angle of elevation = 73°

The distance between the two buildings = 46 m

tan 73° = b/46

tan 73° = 3.27

tan 73° = b/46

3.27 = b/46

b = 3.27 x 46

b = 150.42 m

B)

Angel of depression= 64°

The distance between the two buildings = 46 m

tan 64° = a/46

tan 64° = 2.05

tan 64° a/46

2.05 = a/46

a = 2.05 x 46

a = 94.3 m

The total height of the fire department building = a + b

= 94.3 + 150.42

= 244.72 m

The height of the fire department is 244.72 m