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# Trigonometry Examples

, ,

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

Solve the equation.

Substitute the known values into the equation.

Simplify the numerator.

Raise to the power of .

Raise to the power of .

Raise to the power of .

Multiply by .

Add and .

Subtract from .

Simplify the denominator.

Multiply by .

Multiply by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Evaluate .

Use the law of cosines to find the unknown side of the triangle, given the other two sides and the included angle.

Solve the equation.

Substitute the known values into the equation.

Simplify the numerator.

Raise to the power of .

Raise to the power of .

Raise to the power of .

Multiply by .

Add and .

Subtract from .

Simplify the denominator.

Multiply by .

Multiply by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Evaluate .

The sum of all the angles in a triangle is degrees.

Add and .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

Subtract from .

These are the results for all angles and sides for the given triangle.