Question

If $\tan A=\frac{3}{4}$, then find $\sin A$.

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{4}$
• D. None of these

Answer 1

The correct option is A $\frac{3}{5}$

We know, $tan\left(\Theta \right)=\frac{Opposite}{Adjacent}$

$\tan A=\frac{3}{4}=\frac{P}{B}$

$\Rightarrow H=\sqrt{P^2+B^2}=\sqrt{3^2+4^2}=5$ .... By Pythagoras theorem

$sin\left(\Theta \right)=\frac{Opposite}{Hypotenuse}$

$\Rightarrow \sin A=\frac{P}{H}=\frac{3}{5}$