Chapter SH, Problem 12.10EP

To determine

To find: The side length measures and angle measures.

Answer to Problem 12.10EP

The length measures are $a\approx 9$ and $b\approx 11$ , and angle measures is $B\approx 88°$ .

Explanation of Solution

Given:

The given figure is as follows.

  

Calculation:

Use the Law of Sines to find the missing sides.

  $\begin{array}{c}\frac{\sin 35°}{6}\approx \frac{\sin 57°}{a}\\ a\approx \frac{6\sin 57°}{\sin 35°}\\ x\approx 9\end{array}$

Find the angle $B$ .

  $\begin{array}{c}m\angle B=180°-\left(57°+35°\right)\\ =88°\end{array}$

Use the Law of Cosines $b^2=a^2+c^2-2ac\cos B$ to find the missing side length.

  $\begin{array}{c}{b}^2=9^2+6^2-2\left(9\right)\left(6\right)\cos 88°\\ =113.23085\\ \approx 11\end{array}$

Therefore, the length measures are $a\approx 9$ and $b\approx 11$ , and angle measures is $B\approx 88°$ .