Question

question 3 of 10
in triangle abc, ( mangle a = 81^{circ}, mangle b = 32^{circ} ), and ( b = 40.2 ). use the law of sines to find a. round your answer to the nearest tenth.

a. 21.3
b. 39.7
c. 74.9
d. 69.8

Explanation:

Step1: State the law of sines

The law of sines is \(\frac{a}{\sin A}=\frac{b}{\sin B}\).

Step2: Substitute the given values

We know \(A = 81^{\circ}\), \(B=32^{\circ}\), and \(b = 40.2\). Substituting into the law of sines formula gives \(\frac{a}{\sin81^{\circ}}=\frac{40.2}{\sin32^{\circ}}\).

Step3: Solve for \(a\)

First, find \(\sin81^{\circ}\approx0.9877\) and \(\sin32^{\circ}\approx0.5299\). Then \(a=\frac{40.2\times\sin81^{\circ}}{\sin32^{\circ}}\).

$$
LATEXBLOCK0
$$

Answer:

C. 74.9