Answer
$\sin$ 60$^{\circ}$ = $\frac{\sqrt 3}{2}$
Work Step by Step
$\sin$ 60$^{\circ}$
We must find side $x$ of the 30$^{\circ}$ - 60$^{\circ}$ Right Triangle.
Pythagorean Theorem: $c$$^{2}$ = $a$$^{2}$ + $b$$^{2}$
2$^{2}$ = 1$^{2}$ + $x$$^{2}$
4 = 1 + $x$$^{2}$
x$^{2}$ = 3
x = $\sqrt 3$
Now consider the triangle from the perspective of the 60$^{\circ}$ angle.
Hypotenuse = 2
Opposite = $\sqrt 3$
Adjacent = 1
$\sin$ 60$^{\circ}$ = $\frac{Opposite}{Hypotenuse}$ = $\frac{\sqrt 3}{2}$
Therefore:
$\sin$ 60$^{\circ}$ = $\frac{\sqrt 3}{2}$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ca1eaf6f-fde5-4561-8a77-76bb7c10a4ad/steps_image/small_1475025671.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020004Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2d49220aa162de997fd8d1b49e9c2230649ebda367886765a55ec8ee522ffdc2)