If θ is a acute angle and sin(θ + 18°) = $$\frac{1}{2}{\text{,}}$$ then the value of θ in circular measure is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{sin}}\left( {\theta + {{18}^ \circ }} \right){\text{ = }}\frac{1}{2} \cr & {\text{sin}}\left( {\theta + {{18}^ \circ }} \right) = {\text{sin }}{30^ \circ } \cr & \theta + {18^ \circ } = {30^ \circ } \cr & \therefore \theta = {12^ \circ } \cr & {\text{We know that,}} \cr & {180^ \circ } = \pi \cr & {12^ \circ } = \frac{\pi }{{{{180}^ \circ }}} \times 12 = \frac{\pi }{{15}} \cr} $$