Question

In $△ABC$, if $b=20,c=21$ and $\sin A=\frac{3}{5}$, then $a$ is equal to

• A. $12$
• B. $13$
• C. $14$
• D. $15$

Answer 1

The correct option is B $13$

We have,

$b=20$, $c=21$, $\sin A=\frac{3}{5}$

$\cos A=\frac{4}{5}$.............$[sin²\theta +cos²\theta =1]$

Now,

$\cos A=\frac{b^2+c^2-a^2}{2bc}$

$\Rightarrow \frac{4}{5}=\frac{400+441-a^2}{2\times 20\times 21}$

$\Rightarrow 4\times 8\times 21=841-a^2$

$\Rightarrow a^2=841-32\times 21$

$\Rightarrow a^2=169$

$\Rightarrow a=13$

Hence, this is the answer.