Question

42°

85°
31
Solve for b.
b
b = [?]
Round your final answer
to the nearest tenth.

Answer 1

`\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{b}{\sin(85^o)}=\cfrac{31}{\sin(42^o)}\implies b\sin(42^o)=31\sin(85^o) \\\\\\ b=\cfrac{31\sin(85^o)}{\sin(42^o)}\implies b\approx 46.2`