Chapter 8.4, Problem 44E

To determine

To Find: The value of the missing angles and the sides for the given triangle.

Answer to Problem 44E

The other two sides of the triangle is $B=59.2°$ , $C=23.3°$ and the remaining side of the triangle is $a=8.9$ .

Explanation of Solution

Given:

The value of the angle $A=36°$ , $b=13$ and $c=6$ , then round the angle measure to the nearest minute and side measures to the nearest tenth.

Calculation:

Consider the law of cosine is,

  $a^2=b^2+c^2-2bc\cos A$

Then,

  $\begin{array}{c}{a}^2={\left(13\right)}^2+6^2-2\left(13\right)\left(6\right)\cos 36°\\ =8.9\end{array}$

Consider the law of sine as,

  $\begin{array}{l}\frac{\sin B}{b}=\frac{\sin A}{a}\\ \sin B=\frac{\sin 36°}{8.9}\\ B=59.2°\end{array}$

Again, consider the law of sine as

  $\begin{array}{l}\frac{\sin C}{c}=\frac{\sin A}{a}\\ \sin C=\frac{\sin 36°}{8.9}\\ C=23.3°\end{array}$

Thus, the other two sides of the triangle is $B=59.2°$ , $C=23.3°$ and the remaining side of the triangle is $a=8.9$ .