Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
In a $\triangle \mathrm{ABC}$, if $b=20, c=21$ and $\sin A=\frac{3}{5}$, find $a$.
In $\triangle \mathrm{ABC}, b=20, c=21$ and $\sin A=\frac{3}{5}$.
Using cosine rule, we have
$\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c}$
$\Rightarrow \sqrt{1-\left(\frac{3}{5}\right)^{2}}=\frac{20^{2}+21^{2}-a^{2}}{2 \times 20 \times 21} \quad\left(\cos ^{2} A+\sin ^{2} A=1\right)$
$\Rightarrow \sqrt{\frac{16}{25}}=\frac{400+441-a^{2}}{840}$
$\Rightarrow \frac{4}{5}=\frac{841-a^{2}}{840}$
$\Rightarrow 672=841-a^{2}$
$\Rightarrow a^{2}=841-672=169$
$\Rightarrow a=13$
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