Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
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 $a$.

Solution:

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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