# Angle of Depression and Tangent

Angle of Depression and Tangent

A man on the roof of a building of known height meters is calling to his dog, sitting a distance of meters from the base of the building. The man measures the angle of depression of his line of sight from the horizontal. How far is the dog from the building in terms of and ?

h

d

θ

h

θ

The distance can be calculated using the trigonometric relation for a right triangle: tangent = opposite/adjacent. Therefore, and .

d

tanθ=h/d

d=h/tanθ

Note that occurs as the equal alternate angles of the oblique line crossing parallel lines.

θ