Trigonometry Examples

Solve the Triangle a=40 , b=27 , c=16
, ,
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.
Tap for more steps...
Step 4.1
Simplify the numerator.
Tap for more steps...
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.
Tap for more steps...
Step 4.2.1
Multiply by .
Step 4.2.2
Multiply by .
Step 4.3
Reduce the expression by cancelling the common factors.
Tap for more steps...
Step 4.3.1
Cancel the common factor of and .
Tap for more steps...
Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Cancel the common factors.
Tap for more steps...
Step 4.3.1.2.1
Factor out of .
Step 4.3.1.2.2
Cancel the common factor.
Step 4.3.1.2.3
Rewrite the expression.
Step 4.3.2
Move the negative in front of the fraction.
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.
Tap for more steps...
Step 8.1
Simplify the numerator.
Tap for more steps...
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.
Tap for more steps...
Step 8.2.1
Multiply by .
Step 8.2.2
Multiply by .
Step 8.3
Evaluate .
Step 9
The sum of all the angles in a triangle is degrees.
Step 10
Solve the equation for .
Tap for more steps...
Step 10.1
Add and .
Step 10.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
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.