Question

a tree is 160 feet tall. If Francis is standing 74 ft from the tree what is the angle of elevation from the ground where Francis standing to the top of the tree? Round to the nearest tenth

Answer 1

We shall begin by drawing a sketch of the question.

The diagram shows the position of the tree, which is 160 feet tall, the position of Francis which is 74 feet from the tree. The angle of elevation from the ground where Francis is standing to the top of the tree is angle F. Therefore, angle F is calculated as follows;

`\begin{gathered} \tan F=\frac{\text{opp}}{\text{adj}} \\ \text{The opposite is facing the reference angle, which is F} \\ \text{The adjacent lies between the reference angle and the right angle} \\ \tan F=(160)/(74) \\ \tan F=2.162162\ldots \\ F=65.179458\ldots \\ F=65.2\text{ (to the nearest tenth)} \end{gathered}`

The angle of elevation is 65.2 degrees (approximated to the nearest tenth)