You must know the lengths of the opposing side and the hypotenuse to calculate the sine of an angle. Find the sine using the formula:

## Example 1:

Find the sine of the angle.

### Solution:

## Example 2:

Find the exact value of sin(30).

### Solution:

The exact value of sin(30) is 1/2.

We can show the result in multiple forms:

Exact form: 1/2

Decimal form: 0.5

## Example 3:

XYZ is a right triangle. ∠XYZ = 35∘. Find the length of XY. Your answer should be rounded to the nearest hundredth.

### Solution:

The sine ratio enables us to determine XY, since sine = opposite/hypotenuse.

So, sin 35 = (XY/10)10(sin 35) = XY 10(0.573 58)

Answer: XY = 5.74cm