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?

1 Answer
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 = "height"/"base" = "opposite"/"adjacent".

or, #tan 53.4° = 65/"shadow

or, shadow = 65/(tan 53.4) = 65/1.3465= 48.27 feet

So, length of the shadow = 48.3 feet.