Trigonometry Examples

Solve the Triangle a=4 , b=10 , c=7
, ,
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
Simplify the results.
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Step 4.1
Simplify the numerator.
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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.
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Step 4.2.1
Multiply by .
Step 4.2.2
Multiply by .
Step 4.3
Cancel the common factor of and .
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Step 4.3.1
Factor out of .
Step 4.3.2
Cancel the common factors.
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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
Simplify the results.
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Step 8.1
Simplify the numerator.
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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.
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Step 8.2.1
Multiply by .
Step 8.2.2
Multiply by .
Step 8.3
Reduce the expression by cancelling the common factors.
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Step 8.3.1
Cancel the common factor of and .
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Step 8.3.1.1
Factor out of .
Step 8.3.1.2
Cancel the common factors.
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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
Solve the equation for .
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Step 10.1
Add and .
Step 10.2
Move all terms not containing to the right side of the equation.
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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.