Chapter 12, Problem 12CR

To determine

Find side $\left(b\right)$ of triangle ABC such that $\angle B=90°\angle C=55°,\text{ and }c=12$ .

Answer to Problem 12CR

The triangle ABC has $b\approx 14.6$ , so option (a) is correct.

Explanation of Solution

Given information: The given triangle ABC has $\angle B=90°\angle C=55°,\text{ and }c=12$ .

Calculation: Since the triangle ABC has $\angle B=90°\angle C=55°,\text{ and }c=12$ . And it is right angle at point $\left(B\right)$ . Therefore in triangle ABC by law of sine,

  $\begin{array}{c}\frac{b}{\sin B}=\frac{c}{\sin C}\\ \frac{b}{\sin \left(90\right)}=\frac{\left(12\right)}{\sin \left(55\right)}\mathrm{....}\left(\begin{array}{l}\angle B=90°\angle C=55°,\\ \text{ and }c=12\end{array}\right)\\ \text{or, }b=\frac{\left(12\right)\sin \left(90\right)}{\sin \left(55\right)}\\ b\approx 14.6\end{array}$

Hence the given triangle ABC has $b\approx 14.6$ , so option (a) is correct.