Search any question & find its solution
Question:
Answered & Verified by Expert
In a triangle, if $b=20, c=21$ and $\sin A=\frac{3}{5}$, then $a$ is equal to :
Options:
Solution:
1942 Upvotes
Verified Answer
The correct answer is:
13
We have, $b=20, c=21$ and $\sin A=\frac{3}{5}$
Now, $\cos ^2 A=1-\sin ^2 A=1-\left(\frac{3}{5}\right)^2$
$=1-\frac{9}{25}=\frac{16}{25}$
$\Rightarrow \quad \cos A=\frac{4}{5}$
Now, $\cos A=\frac{b^2+c^2-a^2}{2 b c}$
$\Rightarrow \quad \frac{4}{5}=\frac{(20)^2+(21)^2-a^2}{2 \cdot 20 \cdot 21}$
$\Rightarrow \quad 400+441-a^2=672$
$\Rightarrow \quad a^2=841-672=169$
$\therefore \quad a=13$
Now, $\cos ^2 A=1-\sin ^2 A=1-\left(\frac{3}{5}\right)^2$
$=1-\frac{9}{25}=\frac{16}{25}$
$\Rightarrow \quad \cos A=\frac{4}{5}$
Now, $\cos A=\frac{b^2+c^2-a^2}{2 b c}$
$\Rightarrow \quad \frac{4}{5}=\frac{(20)^2+(21)^2-a^2}{2 \cdot 20 \cdot 21}$
$\Rightarrow \quad 400+441-a^2=672$
$\Rightarrow \quad a^2=841-672=169$
$\therefore \quad a=13$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.