# Angle of Depression and Sine

Angle of Depression and Sine

A man on the roof of a building of known height meters calls to his sitting dog, at a distance of meters away from him through the air. He measures the angle of depression of his line of sight from the horizontal. What is the value of in terms of and ?

h

d

θ

d

h

θ

He uses the trigonometric relation for a right triangle: sine = opposite/hypotenuse. Therefore, and .

sinθ=h/d

d=h/sinθ

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

θ