Chapter 13.5, Problem 52E

To determine

To calculate: The height of the tree.

  

Answer to Problem 52E

The height of the treeis $12.7\text{ m}$ .

Explanation of Solution

Given information:

The shadow of tree is 25 meters long when angle of elevation of sun is $27°$ .

  

Formula used:

In a right triangle the tangent trigonometric function is $\tan \theta =\frac{\text{adjacent}}{\text{side}}$ .

Calculation:

Consider the provided information thatthe shadow of tree is 25 meters long when angle of elevation of sun is $27°$ .

  

Here BC is shadow of the tree and AB is the height of the tree.

In a right triangle the tangent trigonometric function is $\tan \theta =\frac{\text{adjacent}}{\text{side}}$ .

Apply it,

  $\begin{array}{c}\tan 27°=\frac{\text{h}}{\text{25}}\\ h=25\tan 27°\\ h=12.7\end{array}$

Thus, the height of the tree is $12.7\text{ meters}$ .