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?

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Answer 1 · 2016-12-19T09:18:33

#48.3# feet

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.