Chapter 6, Problem 15RE

To determine

To find: The height of the tree.

Answer to Problem 15RE

The height of the tree is $31.01\text{ft}$ .

Explanation of Solution

Given information:

The given figure of the tree is,

  

The base of the triangle is calculated as,

  $\begin{array}{l}\cos 28°=\frac{b}{75}\\ b=66.22\text{ft}\end{array}$

The height of the bottom of the tree from the base is calculated as,

  $\begin{array}{l}\tan 28°=\frac{c}{b}\\ \tan 28°=\frac{c}{66.22}\\ c=35.21\text{ft}\end{array}$

The height of the top of the tree from the base is calculated as,

  $\begin{array}{l}\tan 45°=\frac{a}{b}\\ 1=\frac{a}{66.22}\\ a=66.22\text{ft}\end{array}$

The height of the tree is calculated as,

  $\begin{array}{c}h=a-c\\ =66.22-35.21\\ =31.01\text{ft}\end{array}$

Therefore, the height of the tree is $31.01\text{ft}$ .