evaluate. write your answer in simplified, rationalized form. do not round. sin 60° =

Explanation:

Step1: Recall sine - value of special angle

We know that for a 30 - 60 - 90 right - triangle, if the side opposite the 30 - degree angle is $a$, the side opposite the 60 - degree angle is $\sqrt{3}a$ and the hypotenuse is $2a$. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\theta = 60^{\circ}$, $\sin60^{\circ}=\frac{\sqrt{3}a}{2a}$.

Step2: Simplify the ratio

Canceling out the common factor $a$ in the numerator and denominator, we get $\sin60^{\circ}=\frac{\sqrt{3}}{2}$.

Answer:

$\frac{\sqrt{3}}{2}$