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

Dillard 2021-09-08 Answered
Give all possible answers
\(\displaystyle{m}\angle{C}={36}^{{\circ}},\ {A}{B}={31},\ {B}{C}={24},\) find \(\displaystyle{m}\angle{A}\)

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Expert Answer

Maciej Morrow
Answered 2021-09-09 Author has 4404 answers
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: \(\displaystyle{A}={27}^{{\circ}}\)
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