Question

Determine the missing parts of triangle $ABC$ from the given information.
$A={63}^o,a=10,c=8.9$

Answer 1

By sine rule, we have $\frac{a}{\sin A}=\frac{c}{\sin C}$
$\Rightarrow \sin C=\frac{c}{a}\sin A=\frac{8.9}{10}\sin 63=0.793$
$\Rightarrow C=arc\sin \left(0.793\right)=52.467$ degrees
$\Rightarrow B=180-A-C=180-63-52.467=64.53$ degrees
By sine rule, we get $\frac{a}{\sin A}=\frac{b}{\sin B}$
Therefore, we get $b=10\times \frac{\sin 64.53}{\sin 63}=10.13$