Question

In an equilateral triangle, a perpendicular drawn from one of the vertices to the opposite side as shown.The value of $Sin\theta$ is equal to

• A. $\frac{1}{\sqrt{3}}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. $\frac{1}{3}$

Answer 1

The correct option is C $\frac{1}{2}$


In $△$ABC,
$\angle A=\angle B=\angle C={60}^{\circ }$
since it is equilateral triangle (given)
$\because$ Altitude of an equilateral triangle bisects the angle of vertex
$\therefore \angle BAD={30}^{\circ }$
$Sin\theta =Sin{30}^{\circ }$
$\Rightarrow Sin\theta =\frac{1}{2}$