Chapter 7, Problem 1RE

Use the law of cosines to find the indicated part of each triangle ABC.

Find b if C= 74.2°, c = 96.3 m, B = 39.5°.

To determine

To calculate: The value of side b using provided information and law of sines if $C=74.2°$, $c=96.3\text{m}$, and $B=39.5°$

Answer to Problem 1RE

Solution: $63.7\text{m}$

Explanation of Solution

Given: $C=74.2°$, $c=96.3\text{m}$, and $B=39.5°$

Calculation: Recall the law of sines is defined as:

$\frac{a}{\sin \left(A\right)}=\frac{b}{\sin \left(B\right)}=\frac{c}{\sin \left(C\right)}$

Apply above formula to find value of side b:

$\begin{array}{c}\frac{b}{\sin \left(B\right)}=\frac{c}{\sin \left(C\right)}\\ \frac{b}{\sin \left(39.5°\right)}=\frac{96.3}{\sin \left(74.2°\right)}\\ b=\sin \left(39.5°\right)\times \frac{96.3}{\sin \left(74.2°\right)}\end{array}$

Solve further with the help of calculator,

$\begin{array}{c}b=\sin \left(39.5°\right)\times \frac{96.3}{\sin \left(74.2°\right)}\\ =0.6361\times \frac{96.3}{0.9622}\\ =63.66\\ \approx 63.7\text{m}\end{array}$

The value of side b is $63.7\text{m}$.