Chapter 10.6, Problem 29P

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

A 60° angle has an adjacent leg 5 cm long. How long is the hypotenuse?

To determine

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

Answer to Problem 29P

The length of the hypotenuse is 10 cm to the nearest tenth

Explanation of Solution

Given information:

The ${60}^{\circ }$ angle has an adjacent leg 5 cm long

Formula used:

  $\cos \theta =\frac{\text{Base}}{\text{Hypotenuse}}$

Calculation:

For a triangle, assume hypotenuse as $AB$ and base as $BC$

The adjacent leg $=BC$$=5\text{ cm}$

The length of the hypotenuse of a triangle can be calculated as,

  $\begin{array}{l}\cos {60}^{\circ }=\frac{\text{Base}}{\text{Hypotenuse}}\\ \cos {60}^{\circ }=\frac{BC}{AB}\\ \cos {60}^{\circ }=\frac{5}{AB}\\ AB=\frac{5}{\cos {60}^{\circ }}\\ AB=\frac{5}{\frac{1}{2}}\\ AB=5\times 2\\ AB=10\text{ cm }\left[\text{Nearest tenth}\right]\end{array}$

Therefore, the length of the hypotenuse is 10 cm to the nearest tenth