Question

Solve for X in the triangle, round to the nearest tenth. 7m, 5m, 53°

Answer 1

`\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(x)}{5}=\cfrac{\sin(53^o)}{7}\implies \sin(x)=\cfrac{5\sin(53^o)}{7} \\\\\\ x=\sin^(-1)\left( \cfrac{5\sin(53^o)}{7} \right)\implies x\approx 34.8^o`