Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$I n a Δ A B C, i f b = 20, c = 21 a n d s i n A = \frac{3}{5}, f i n d a .$

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Solution

$b = 20, c = 21 a n d s i n A = \frac{3}{5} c o s A = \frac{4}{5} c o s A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \Rightarrow \frac{4}{5} = \frac{20^{2} + 21^{2} - a^{2}}{2 \times 20 \times 21} \Rightarrow \frac{4}{5} = \frac{20^{2} + 21^{2} - a^{2}}{2 \times 20 \times 21} \Rightarrow 2 \times 4 \times 4 \times 21 = 841 - a^{2} \Rightarrow 672 = 841 - a^{2} \Rightarrow a^{2} = 841 - 672 \Rightarrow a^{2} = 169 \Rightarrow a = 13$

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