Chapter 12.8, Problem 14OE

To determine

Give the name of law that can be used first to solve the triangle if the measurements are $a=9,b=10\text{ and }\angle B=40°$ .

Answer to Problem 14OE

The law of sine is used for triangle which has $a=9,b=10\text{ and }\angle B=40°$ .

Explanation of Solution

Given information: The given measurements of triangle are $a=9,b=10\text{ and }\angle B=40°$ .

Calculation: Since the given triangle has $b=20,c=18\text{ and }\angle B=120°$ . Therefore the given triangle has the case of SSA (side-side-angle) where $\left(\angle B\right)$ is opposite angle to side $\left(b\right)$ . Therefore first apply law of sine for angle $\left(\angle B\right)$ to find the missing angle $\left(\angle A\right)$ and then other formulas can be used to determine the remaining parameters of the given triangle.