Question

You are standing 20 feet away from a tree that is 45 feet tall. What is the angle of elevation to the top of the tree? (round to the nearest degree)

Answer 1

Consider the schematic diagram given below,

In the diagram, AB represents the height of the tree, and point C is the location of the observer.

The angle of of elevation to the top of the tree is the angle BCA here.

This angle can be calculated as,

`\begin{gathered} \tan (\angle BCA)=(AB)/(BC) \\ \tan (\angle BCA)=(45)/(20) \\ \tan (\angle BCA)=2.25 \end{gathered}`

Taking the inverse function both sides,

`\begin{gathered} \angle BCA=\tan ^(-1)(2.25) \\ \angle BCA\approx66^(\circ) \end{gathered}`

Thus, the required angle of elevation is approximately 66 degrees.