Chapter 10.6, Problem 31P

For each triangle, find the missing side length to the nearest tenth.

A 5° angle has an opposite leg 2 ft long. How long is the adjacent leg?

To determine

To calculate: The length of the adjacent leg for each triangle to the nearest tenth

Answer to Problem 31P

The length of the adjacent side of leg is 23 feet to the nearest tenth

Explanation of Solution

Given information:

The $5^{\circ }$ angle has an opposite leg 2 feet long

Formula used:

  $\tan \theta =\frac{\text{Perpendicular}}{\text{Base}}$

Calculation:

For a triangle, assume base as $BC$ and perpendicular as $AC$

The opposite leg $=AC$$=2$ feet

The adjacent leg $=BC$

The length of the adjacent leg of a triangle can be calculated as,

  $\begin{array}{l}\tan 5^{\circ }=\frac{\text{Perpendicular}}{\text{Base}}\\ \tan 5^{\circ }=\frac{AC}{BC}\\ \tan 5^{\circ }=\frac{2}{BC}\\ BC=\frac{2}{\tan 5^{\circ }}\\ BC=\frac{2}{0.087}\\ BC=22.98\\ BC=23.0\text{ feet }\left[\text{Rounded to the nearest tenth}\right]\end{array}$

Therefore, the length of the adjacent side of leg is 23 feet to the nearest tenth