Question

In the diagram below, a point is located 30 feet from the base of a tree. The angle of elevation from the point on the ground to the top of the tree is 57°. What is the height of the tree to the nearest foot?

Answer 1

Data:

`\begin{gathered} x=30 \\ \theta=57 \end{gathered}`

Then, using the tangent function:

`\begin{gathered} \tan (\theta)=(Opposite)/(Adjacent) \\ \text{Opposite}=\text{height}=\tan (\theta)* Adjacent \end{gathered}`

Replacing the values:

`\begin{gathered} \text{Height}=\tan (57)*30=1.53*30=45.9 \\ \text{Height}\approx46 \end{gathered}`

The answer of height to the nearest foot: 46ft