In a , if b = 20, c = 21 and =3 5 , find a. - Vidyadip

Question

In a $\triangle\text{ABC},$ if b = 20, c = 21 and $\sin\text{A}=\frac{3}{5},$ find a.

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Answer

$\text{b = 20, c = 21,}\sin\text{A}=\frac{3}{5}$
$\cos\text{A}=\frac{4}{5}$
$\cos\text{A}=\frac{\text{b}^2+\text{c}^2-\text{a}^2}{2\text{bc}}$
$\Rightarrow\frac{4}{5}=\frac{20^2+21^2-\text{a}^2}{2\times20\times21}$
$\Rightarrow2\times4\times4\times21=841-\text{a}^2$
$\Rightarrow672=841-\text{a}^2$
$\Rightarrow\text{a}^2=841-672$
$\Rightarrow\text{a}^2=169$
$\Rightarrow\text{a}=13$

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