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# Trigonometry Examples

, ,

Step 1

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

Step 2

Solve the equation.

Step 3

Substitute the known values into the equation.

Step 4

Step 4.1

Simplify the numerator.

Step 4.1.1

Raise to the power of .

Step 4.1.2

Raise to the power of .

Step 4.1.3

Raise to the power of .

Step 4.1.4

Multiply by .

Step 4.1.5

Add and .

Step 4.1.6

Subtract from .

Step 4.2

Simplify the denominator.

Step 4.2.1

Multiply by .

Step 4.2.2

Multiply by .

Step 4.3

Cancel the common factor of and .

Step 4.3.1

Factor out of .

Step 4.3.2

Cancel the common factors.

Step 4.3.2.1

Factor out of .

Step 4.3.2.2

Cancel the common factor.

Step 4.3.2.3

Rewrite the expression.

Step 4.4

Evaluate .

Step 5

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

Step 6

Solve the equation.

Step 7

Substitute the known values into the equation.

Step 8

Step 8.1

Simplify the numerator.

Step 8.1.1

Raise to the power of .

Step 8.1.2

Raise to the power of .

Step 8.1.3

Raise to the power of .

Step 8.1.4

Multiply by .

Step 8.1.5

Add and .

Step 8.1.6

Subtract from .

Step 8.2

Simplify the denominator.

Step 8.2.1

Multiply by .

Step 8.2.2

Multiply by .

Step 8.3

Reduce the expression by cancelling the common factors.

Step 8.3.1

Cancel the common factor of and .

Step 8.3.1.1

Factor out of .

Step 8.3.1.2

Cancel the common factors.

Step 8.3.1.2.1

Factor out of .

Step 8.3.1.2.2

Cancel the common factor.

Step 8.3.1.2.3

Rewrite the expression.

Step 8.3.2

Move the negative in front of the fraction.

Step 8.4

Evaluate .

Step 9

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

Step 10

Step 10.1

Add and .

Step 10.2

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

Step 10.2.1

Subtract from both sides of the equation.

Step 10.2.2

Subtract from .

Step 11

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