Question

If $\tan x=\frac{3}{4},0<x<{90}^{\circ },$ then what is the value of $\sin x?$

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{12}{25}$
• D. $\frac{13}{25}$

Answer 1

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

Given that,

$\tan x=\frac{3}{4}$ for $0<x<{90}^o$.

To find out,

The value of $\sin x$.

We know that, $\tan \theta =\frac{\text{Opposite Side}}{\text{Adjacent Side}}$

Let the adjacent side be $B$, opposite side be $P$ and the hypotenuse be $H$.

Hence, $\frac{P}{B}=\frac{3}{4}$
Thus, $P=3,B=4$

For a right angled triangle, we know that, $H^2=P^2+B^2$
Hence, $H^2=3^2+4^2$
$\Rightarrow H^2=25$

$\Rightarrow H^2=5^2$
$\Rightarrow H=5$
Now, we also know that, $\sin \theta =\frac{\text{Opposite Side}}{\text{Hypotenuse}}$

Hence, $\sin x=\frac{P}{H}$

$=\frac{3}{5}$

Hence, $\sin x=\frac{3}{5}$.