Question

question 9 of 25
in triangle abc, m∠a = 35°, m∠b = 65°, and a = 8.71. use the law of sines to find b. round your answer to the nearest tenth.
a. 9.5
b. 23.7
c. 8.7
d. 13.8

Explanation:

Step1: Recall law of sines formula

$\frac{a}{\sin A}=\frac{b}{\sin B}$

Step2: Substitute given values

$\frac{8.71}{\sin35^{\circ}}=\frac{b}{\sin65^{\circ}}$

Step3: Solve for b

$b = \frac{8.71\times\sin65^{\circ}}{\sin35^{\circ}}$
$\sin35^{\circ}\approx0.574$, $\sin65^{\circ}\approx0.906$
$b=\frac{8.71\times0.906}{0.574}=\frac{7.89126}{0.574}\approx13.8$

Answer:

D. 13.8