Angle of Depression and Tangent

height of building h (m)

80

angle of depression θ (°)

50

A man on the roof of a building of known height

h

meters is calling to his dog, sitting a distance of

d

meters from the base of the building. The man measures the angle of depression

θ

of his line of sight from the horizontal. How far is the dog from the building in terms of

h

and

θ

?

The distance

d

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

tanθ=h/d

and

d=h/tanθ

.

Note that

θ

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