Question

A billboard d=85 feet wide is perpendicular to a straight road and is 40 feet from the road. Find the point on the road at which angle θ subtended by the billboard is a maximum. (Round answer to 2 decimal places).

Answer 1

I know that so far...

Answer 2

Angle on the left = alpha, the one on the right is theta.

Answer 3

\[\tan \alpha = \frac{ 40 }{ x }\]\[\tan(\alpha+\theta) = \frac{ 40+85 }{ x }=\frac{ 125 }{ x }\]\[\tan (\alpha + \theta) = \frac{ \tan(\alpha) + \tan(\theta) }{ 1- \tan(\alpha) \tan(\theta)}\]