Question

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

Answer 1

Answer:

The shadow length is 125 inches.

Step-by-step explanation:

The triangle that the sun's rays and the fence post form is shown in the figure.

From trigonometry we know that $tan(30^o)$ is the ratio of the opposite (72-in fence) to the adjacent side $L$ of the triangle (the shadow length):

$tan(30^o) = \dfrac{72 in}{L}$

since

$tan(30^o) = \dfrac{\sqrt{3} }{3}$

we have

$\dfrac{\sqrt{3} }{3} = \dfrac{72 in}{L}$

solving for $L$ we get:

$L = 72\sqrt{3}\\\\\boxed{L = 124.71\: in.}$

Hence, the length of the shadow to the nearest inch is 125 inches.