Question

D. 18.3 Math question no Guessing and Please show work

Answer 1

To solve this we can apply the law of sines. WIth law of sines, we have:

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

So, we do not know B, c or C. To find either angle or side c, we hav to find angle B first and the rest will follow. To find angle B, we can do:

$\frac{\sin{15}}{9}=\frac{\sin{B}}{10} \implies \\ \frac{10\sin{15}}{9}=\sin{B} \implies\\ .29=\sin{B} \implies \sin^{-1}(.288)=B \implies\\ 16.77^{\circ}=B$

So, we have $A=15^{\circ}, B=16.77^{\circ} \implies\\ A+B+C=180 \implies \\ C=180-(A+B)=180-31.77=148.23$

So, we have to solve:

$\frac{\sin{16.77}}{10}=\frac{\sin{148.23}}{c} \implies \\ c=\frac{\sin(148.23)*10}{\sin{16.77}} \implies\\ c\approx 18.2480088$