# Precalculus Examples

The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.

Substitute the name of each side into the definition of the sine function.

Set up the equation to solve for the hypotenuse, in this case .

Substitute the values of each variable into the formula for sine.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Combine.

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Multiply and .

Multiply by .

Divide by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form: