Question

Determine the missing parts of triangle $ABC$ from the given information.
$A={40}^o,a=20,b=15$

Answer 1

• By sine rule , we have $\frac{a}{\sin A}=\frac{b}{\sin B}$
• Which gives $\sin B=\frac{b}{a}\sin A=\frac{3}{4}\sin 40=0.482$
• Therefore $B=arc\sin \left(0.482\right)=28.82$ degrees
• Which implies $C=180-A-B=180-40-28.82=111.18$ degrees
• By sine rule , we get $\frac{a}{\sin A}=\frac{c}{\sin C}$
• Therefore we get $c=20\times \frac{\sin 111.18}{\sin 40}=29.01$