Chapter SH, Problem 12.14EP

To determine

To find: The angles measures of the given triangle.

Answer to Problem 12.14EP

The angles measures are $A\approx 135°$ , $B\approx 15°$ and $C\approx 30°$ .

Explanation of Solution

Given:

The given triangle is as follows.

  

Calculation:

Use the Law of Cosines to find the missing side length.

  $\begin{array}{c}{a}^2=b^2+c^2-2bc\cos A\\ 2\left(5\right)\left(10\right)\cos A=5^2+{10}^2-{14}^2\\ \cos A=-\frac{71}{100}\\ A\approx 135°\end{array}$

Use the Law of Sines to find the missing angles.

  $\begin{array}{c}\frac{\sin B}{5}\approx \frac{\sin 135°}{14}\\ \sin B\approx \frac{5\sin 135°}{14}\\ B\approx 15°\end{array}$

Find the other angle $C$ .

  $\begin{array}{c}m\angle C\approx 180°-\left(135°+15°\right)\\ \approx 30°\end{array}$

Therefore, the angles measures are $A\approx 135°$ , $B\approx 15°$ and $C\approx 30°$ .