Question

The cosine law

How do I figure out which formula I'd use for this question?

B= 88 degrees, a= 31.5m, c= 25.6, B= 39. 9

Answer 1

`\bf \textit{Law of sines} \\ \quad \\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c}\\\\ -------------------------------\\\\`


`\bf \cfrac{sin(88^o)}{39.9}=\cfrac{sin(A)}{31}\implies \cfrac{31\cdot sin(88^o)}{39.9}=sin(A) \\\\\\ sin^(-1)\left[ \cfrac{31\cdot sin(88^o)}{39.9} \right]=sin^(-1)\left[ sin(A) \right] \\\\\\ sin^(-1)\left[ \cfrac{31\cdot sin(88^o)}{39.9} \right]=\measuredangle A \\\\\\ 50.93841^o\approx \measuredangle A\qquad thus\qquad \measuredangle C\approx 41.0619^o`