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