what is the exact value of $\\sin 60^{\\circ}$?\n\nenter your answer as a fraction in simplest form by…
what is the exact value of $\\sin 60^{\\circ}$?\n\nenter your answer as a fraction in simplest form by filling in the boxes.
Answer
Explanation:
Step1: Identify the special right triangle
A $60^{\circ}$ angle is part of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle.
Step2: Determine side length ratios
In this triangle, the sides are $x$, $x\sqrt{3}$, and $2x$.
Step3: Apply the sine definition
The sine of an angle is $\frac{\text{opposite}}{\text{hypotenuse}}$. $$ \sin 60^{\circ} = \frac{x\sqrt{3}}{2x} $$
Step4: Simplify the fraction
Cancel the common factor $x$ from the numerator and denominator. $$ \sin 60^{\circ} = \frac{\sqrt{3}}{2} $$
Answer:
\frac{\sqrt{3}}{2}