Question

If $\sin \theta =\frac{5}{13}$, where $\theta$ is an acute angle, then find the value of $\cos \theta$.

Answer 1

Given : $\sin \theta =\frac{5}{13}$
To find : $\cos \theta =$?
We know that,
$\sin \theta =\frac{P}{H}=\frac{AB}{AC}=\frac{5}{13}$
According to Pythagoras theorem, we get
$P^2+B^2=H^2$
$\Rightarrow {\left(5\right)}^2+B^2={\left(13\right)}^2$
$\Rightarrow B^2=169-25$
$\Rightarrow B^2=144$
$\Rightarrow B=12=BC$
$\Rightarrow \cos \theta =\frac{B}{H}=\frac{BC}{AC}=\frac{12}{13}$
$\cos \theta =\frac{12}{13}$