Precalculus Examples

Step 1
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.
Step 2
Substitute the name of each side into the definition of the sine function.
Step 3
Set up the equation to solve for the hypotenuse, in this case .
Step 4
Substitute the values of each variable into the formula for sine.
Step 5
Multiply the numerator by the reciprocal of the denominator.
Step 6
Multiply by .
Step 7
Combine and simplify the denominator.
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Step 7.1
Multiply by .
Step 7.2
Raise to the power of .
Step 7.3
Raise to the power of .
Step 7.4
Use the power rule to combine exponents.
Step 7.5
Add and .
Step 7.6
Rewrite as .
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Step 7.6.1
Use to rewrite as .
Step 7.6.2
Apply the power rule and multiply exponents, .
Step 7.6.3
Combine and .
Step 7.6.4
Cancel the common factor of .
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Step 7.6.4.1
Cancel the common factor.
Step 7.6.4.2
Rewrite the expression.
Step 7.6.5
Evaluate the exponent.
Step 8
Cancel the common factor of .
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Step 8.1
Factor out of .
Step 8.2
Cancel the common factor.
Step 8.3
Rewrite the expression.
Step 9
Multiply by .
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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