Chapter 10.6, Problem 26P

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

A 25° angle has an opposite leg 6 cm long. How long is the adjacent leg?

To determine

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

Answer to Problem 26P

The length of adjacent leg is 12.9 cm to the nearest tenth

Explanation of Solution

Given information:

The ${25}^{\circ }$ angle has an opposite leg 6cm long

Formula used:

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

Calculation:

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

The adjacent leg = BC

Opposite leg of ${25}^{\circ }$ angle = AC

The missing side length can be calculated as,

  $\begin{array}{l}\tan {25}^{\circ }=\frac{\text{Perpendicular}}{\text{Base}}\\ \tan {25}^{\circ }=\frac{AC}{BC}\\ \tan {25}^{\circ }=\frac{6}{BC}\\ BC=\frac{6}{0.466}\\ BC=12.87\\ BC=12.9\left[\text{Rounded to the nearest tenth}\right]\end{array}$

Therefore, the length of adjacent leg is 12.9 cm to the nearest tenth