# The sun casts a shadow of a pine tree on the ground. The tree is 65 feet tall. The angle of depression is 53.4°. What is the length of the shadow?

Dec 19, 2016

$48.3$ feet

#### Explanation:

Here height of the tree, its shadow and ground form a right angled triangle.

Angle of depression = angle of elevation = 53.4°

Therefore $\tan 53.4 = \text{height"/"base" = "opposite"/"adjacent}$.

or, shadow = $\frac{65}{\tan 53.4} = \frac{65}{1.3465} = 48.27$ feet
So, length of the shadow = $48.3$ feet.