Chapter 72, Problem 1A

To determine

The length of side x.

Answer to Problem 1A

The length of side x is $x=37.367\text{inch}$

Explanation of Solution

Given information:

The given figure is

  

Calculation:

Intriangle ABC, the length of side AB can be calculated from sine rule.

  $\begin{array}{l}\frac{\sin A}{BC}=\frac{\sin B}{AC}=\frac{\sin C}{AB}\\ \frac{\sin 52°30\text{'}}{65.299}=\frac{\sin B}{AC}=\frac{\sin 27°00\text{'}}{x}\end{array}$

  $\begin{array}{l}\frac{\sin 52°30\text{'}}{65.299}=\frac{\sin 27°00\text{'}}{x}\\ x=\sin 27°00\text{'}\times \frac{65.299}{\sin 52°30\text{'}}\\ x=37.367\text{inch}\end{array}$

Conclusion:

Thus, the length of side d is $x=37.367\text{inch}$