Question

Find the value of $\theta$ in degrees for $2{\sin }^2\theta =\frac{1}{2}$ if $\theta$ is one of the angles of an acute angled triangle.

Answer 1

$2{\sin }^2\theta =\frac{1}{2}\Rightarrow {\sin }^2\theta =\frac{1}{4}\Rightarrow \sin \theta =\pm \frac{1}{2}$

Since, $\theta$ is acute

$\sin \theta =\frac{1}{2}\Rightarrow \theta ={30}^o$