Question

If $\sin \theta =\frac{7}{23}$, where $\theta$ is an acute angle, find the value of $\cos \theta$.

Answer 1

Given: $\sin \theta =\frac{7}{25}$
To find: $\cos =?$
We know that,
$\sin \theta =\frac{P}{H}=\frac{AB}{AC}=\frac{7}{25}$
According to Pythagoras theorem,
$P^2+B^2=H^2$
$(7{)}^2+B^2=(25{)}^2$
$49+B^2$
$B^2=615-49$
$B^2=576$
$B=24$
$\cos \theta =\frac{B}{H}=\frac{BC}{AC}=\frac{24}{25}$
$\cos \theta =\frac{24}{25}$