Question

question 17 of 25 use the law of sines to find the length of side c. a 46.7° b c b 48° 44 c a. 44.93 b. 43.09 c. 60.26 d. 44

Explanation:

Step1: Recall law of sines

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

Step2: Identify known values

We know $C = 48^{\circ}$, $c$ is unknown, $a = 44$, $A=46.7^{\circ}$

Step3: Set up proportion

$\frac{c}{\sin C}=\frac{a}{\sin A}$, so $c=\frac{a\sin C}{\sin A}$

Step4: Substitute values

$c=\frac{44\times\sin(48^{\circ})}{\sin(46.7^{\circ})}$

Step5: Calculate

$\sin(48^{\circ})\approx0.7431$, $\sin(46.7^{\circ})\approx0.7285$, $c=\frac{44\times0.7431}{0.7285}=\frac{32.6964}{0.7285}\approx44.93$

Answer:

A. 44.93