Question

solve for a. a = ? round your final answer to the nearest tenth. law of sines: $\frac{a}{sin a}=\frac{b}{sin b}=\frac{c}{sin c}$

Explanation:

Step1: Identify values for law of sines

Let $a$ be the unknown side, $A = 42^{\circ}$, $b = 22$, and $B=23^{\circ}$. According to the law of sines $\frac{a}{\sin A}=\frac{b}{\sin B}$.

Step2: Rearrange for $a$

Cross - multiply to get $a=\frac{b\sin A}{\sin B}$.

Step3: Substitute values

Substitute $b = 22$, $\sin A=\sin(42^{\circ})\approx0.6691$, and $\sin B=\sin(23^{\circ})\approx0.3907$ into the formula: $a=\frac{22\times0.6691}{0.3907}$.

Step4: Calculate $a$

$22\times0.6691 = 14.7202$, then $\frac{14.7202}{0.3907}\approx37.7$.

Answer:

$37.7$