Question

The diagram shows angle abc

Answer 1

Check the picture below.

`\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle C)}{c}\implies \cfrac{c\cdot sin(\measuredangle A)}{a}=sin(\measuredangle C) \\\\\\ sin^(-1)\left[ \cfrac{c\cdot sin(\measuredangle A)}{a} \right]=\measuredangle C\implies sin^(-1)\left[ \cfrac{8.2\cdot sin(81^o)}{13.5} \right]=\measuredangle C`

`36.86^o\approx C\hspace{15em}\stackrel{180-81-36.86}{\measuredangle B\approx 62.14^o} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}\implies b\cdot sin(\measuredangle A)=a\cdot sin(\measuredangle B)\implies b=\cfrac{a\cdot sin(\measuredangle B)}{sin(\measuredangle A)} \\\\\\ b=\cfrac{13.5\cdot sin(62.14^o)}{sin(81^o)}\implies \boxed{b\approx 12.08}`

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