Chapter 12.8, Problem 9OE

To determine

Give the name of law that can be used first to solve the triangle if the measurements are $b=15,\angle B=100°\text{ and }\angle C=25°$ .

Answer to Problem 9OE

The law of sine is used for triangle which has $b=15,\angle B=100°\text{ and }\angle C=25°$ .

Explanation of Solution

Given information: The given measurements of triangle are $b=15,\angle B=100°\text{ and }\angle C=25°$ .

Calculation: Since the given triangle has $a=17,\angle B=20°\text{ and }\angle C=60°$ . Therefore the given triangle has the case of ASA (angle-side-angle) where (S) is the non-included side between the given two angles. Therefore first evaluate the third angle $\left(\angle A\right)$ by the method $\angle A=190-\angle B-\angle C$ and then with the help of law of sine other sides can be evaluated.

The law of sine is stated in general form as,

  $\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}=\frac{1}{2R}\mathrm{....}\left(R\text{ is circumradius}\right)$