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

The shadow length is 125 inches.

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) = (72 in)/(L)`

since

`tan(30^o) = (√(3) )/(3)`

we have

`(√(3) )/(3) = (72 in)/(L)`

solving for
`L` we get:

`L = 72√(3)\\\\\boxed{L = 124.71\: in.}`

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