Question

Use the Law of Sines to find the measure of angle J to the nearest degree.

Answer 1

$\bf \textit{Law of sines} \\ \quad \\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\ -----------------------------\\\\ \cfrac{sin(J)}{9.1}=\cfrac{sin(97^o)}{11}\implies sin(J)=\cfrac{9.1\cdot sin(97^o)}{11} \\\\\\ \textit{now taking }sin^{-1}\textit{ to both sides} \\\\\\ sin^{-1}\left[ sin(J) \right]=sin^{-1}\left( \cfrac{9.1\cdot sin(97^o)}{11} \right) \\\\\\ \measuredangle J=sin^{-1}\left( \cfrac{9.1\cdot sin(97^o)}{11} \right)$