# 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 = 3 5 - Mathematics

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 $\sin A = \frac{3}{5}$

#### Solution

In ∆ABC, b = 20, c = 21 and $\sin A = \frac{3}{5}$

Using cosine rule, we have

$\cos A = \frac{b^2 + c^2 - a^2}{2bc}$
$\Rightarrow \sqrt{1 - \left( \frac{3}{5} \right)^2} = \frac{{20}^2 + {21}^2 - a^2}{2 \times 20 \times 21} \left( \cos^2 A + \sin^2 A = 1 \right)$
$\Rightarrow \sqrt{\frac{16}{25}} = \frac{400 + 441 - a^2}{840}$
$\Rightarrow \frac{4}{5} = \frac{841 - a^2}{840}$
$\Rightarrow 672 = 841 - a^2$

$\Rightarrow a^2 = 841 - 672 = 169$
$\Rightarrow a = 13$

Concept: Sine and Cosine Formulae and Their Applications
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 10 Sine and cosine formulae and their applications
Q 4 | Page 26