Question

The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building

Answer 1

Let the height of the first building AD be x m

∴ EC = 120 – x

In the right ∆CDE,

tan 45° = `"CE"/"CD"`

1 = `(120 - x)/70`

⇒ 70 = 120 – x

x = 50 cm

∴ The height of the first building is 50 m