# Give all possible answers m\angle C=36^{\circ},\ AB=31,\ BC=24, find P

$$\displaystyle{m}\angle{C}={36}^{{\circ}},\ {A}{B}={31},\ {B}{C}={24},$$ find $$\displaystyle{m}\angle{A}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself.

Maciej Morrow
Step 1
Given
$$\displaystyle{m}\angle{C}={36}^{{\circ}},\ {A}{B}={31},\ {B}{C}={24}$$
By sine law,
$$\displaystyle{\frac{{{A}{B}}}{{{\sin{{C}}}}}}={\frac{{{B}{C}}}{{{\sin{{A}}}}}}$$
$$\displaystyle{\frac{{{31}}}{{{\sin{{36}}}^{{\circ}}}}}={\frac{{{24}}}{{{\sin{{A}}}}}}$$
$$\displaystyle{\sin{{A}}}={\frac{{{24}}}{{{31}}}}{{\sin{{36}}}^{{\circ}}=}{0.45506}$$
$$\displaystyle{A}={\arcsin{{\left({0.45506}\right)}}}$$
$$\displaystyle{A}={27}^{{\circ}}$$
Answer: $$\displaystyle{A}={27}^{{\circ}}$$