Question

The sun shines at a 30° angle to the ground. To the nearest inch, how long is the shadow cast by a 72-in. tall fence post?

Answer 1

The length of the shadow is 124.7 in

Explanation:

Given:

Angle, θ = 30°

Height of the fence,  h = 72 in

Length of the shadow, l = ?

Given:

tan 30° = $\frac{perpendicular}{base} = \frac{height of the fence}{length of the shadow}$

$\frac{1}{\sqrt{3} } = \frac{72}{l} \\\\l = 72\sqrt{3} \\\\l = 124.7 in$

Therefore, the length of the shadow is 124.7 in