Question

Answer each of 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 $\sin A=\frac{3}{5}$, find a.

Answer 1

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

Using cosine rule, we have

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

$$\begin{gathered} \Rightarrow a^2=841-672=169 \\ \Rightarrow a=13 \end{gathered}$$