Dillard

2021-09-08

Give all possible answers

$m\mathrm{\angle}C={36}^{\circ},\text{}AB=31,\text{}BC=24,$ find $m\mathrm{\angle}A$

Maciej Morrow

Skilled2021-09-09Added 98 answers

Step 1

Given

$m\mathrm{\angle}C={36}^{\circ},\text{}AB=31,\text{}BC=24$

By sine law,

$\frac{AB}{\mathrm{sin}C}=\frac{BC}{\mathrm{sin}A}$

$\frac{31}{{\mathrm{sin}36}^{\circ}}=\frac{24}{\mathrm{sin}A}$

$\mathrm{sin}A=\frac{24}{31}{\mathrm{sin}36}^{\circ}=0.45506$

$A=\mathrm{arcsin}\left(0.45506\right)$

$A={27}^{\circ}$

Answer:$A={27}^{\circ}$

Given

By sine law,

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