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In an equilateral triangle of side $2a$, a perpendicular is drawn from one vertex to the opposite side, forming a $30^\circ$-$60^\circ$-$90^\circ$ triangle as shown. What is $\sin 30^\circ$? 
A$\frac{1}{2}$
B$\frac{\sqrt{3}}{2}$
C$\frac{1}{\sqrt{3}}$
D$\sqrt{3}$
Answer & Solution
Correct answer: A. $\frac{1}{2}$
The perpendicular bisects the base, so in the right triangle formed, the hypotenuse is $2a$ and the side opposite $30^\circ$ is $a$. Hence $\sin 30^\circ=\frac{a}{2a}=\frac{1}{2}$.
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