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:

Angle of sun to the ground, θ = 30°

Height of the fence, h = 72 in

Length of the shadow, l = ?

We know,

tan θ = (Perpendicular)/(Base)  

So,

tan 30° = $\frac{72}{l}$

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

Therefore, the length of the shadow is 124.7 in