Trigonometry Examples

, ,
Step 1
The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.
Step 2
Substitute the known values into the law of sines to find .
Step 3
Solve the equation for .
Tap for more steps...
Step 3.1
Factor each term.
Tap for more steps...
Step 3.1.1
The exact value of is .
Step 3.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.1.3
Multiply by .
Step 3.1.4
Evaluate .
Step 3.1.5
Divide by .
Step 3.2
Find the LCD of the terms in the equation.
Tap for more steps...
Step 3.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2.2
The LCM of one and any expression is the expression.
Step 3.3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 3.3.1
Multiply each term in by .
Step 3.3.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.1
Rewrite using the commutative property of multiplication.
Step 3.3.2.2
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.2.1
Factor out of .
Step 3.3.2.2.2
Cancel the common factor.
Step 3.3.2.2.3
Rewrite the expression.
Step 3.3.2.3
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.3.1
Cancel the common factor.
Step 3.3.2.3.2
Rewrite the expression.
Step 3.3.3
Simplify the right side.
Tap for more steps...
Step 3.3.3.1
Multiply by .
Step 3.4
Solve the equation.
Tap for more steps...
Step 3.4.1
Rewrite the equation as .
Step 3.4.2
Divide each term in by and simplify.
Tap for more steps...
Step 3.4.2.1
Divide each term in by .
Step 3.4.2.2
Simplify the left side.
Tap for more steps...
Step 3.4.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.4.2.2.1.1
Cancel the common factor.
Step 3.4.2.2.1.2
Divide by .
Step 3.4.2.3
Simplify the right side.
Tap for more steps...
Step 3.4.2.3.1
Evaluate the root.
Step 3.4.2.3.2
Divide by .
Step 4
The sum of all the angles in a triangle is degrees.
Step 5
Solve the equation for .
Tap for more steps...
Step 5.1
Add and .
Step 5.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Subtract from .
Step 6
The law of sines is based on the proportionality of sides and angles in triangles. The law states that for the angles of a non-right triangle, each angle of the triangle has the same ratio of angle measure to sine value.
Step 7
Substitute the known values into the law of sines to find .
Step 8
Solve the equation for .
Tap for more steps...
Step 8.1
Factor each term.
Tap for more steps...
Step 8.1.1
Evaluate .
Step 8.1.2
Evaluate .
Step 8.1.3
Divide by .
Step 8.2
Find the LCD of the terms in the equation.
Tap for more steps...
Step 8.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 8.2.2
The LCM of one and any expression is the expression.
Step 8.3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 8.3.1
Multiply each term in by .
Step 8.3.2
Simplify the left side.
Tap for more steps...
Step 8.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 8.3.2.1.1
Cancel the common factor.
Step 8.3.2.1.2
Rewrite the expression.
Step 8.4
Solve the equation.
Tap for more steps...
Step 8.4.1
Rewrite the equation as .
Step 8.4.2
Divide each term in by and simplify.
Tap for more steps...
Step 8.4.2.1
Divide each term in by .
Step 8.4.2.2
Simplify the left side.
Tap for more steps...
Step 8.4.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 8.4.2.2.1.1
Cancel the common factor.
Step 8.4.2.2.1.2
Divide by .
Step 8.4.2.3
Simplify the right side.
Tap for more steps...
Step 8.4.2.3.1
Divide by .
Step 9
These are the results for all angles and sides for the given triangle.
Enter YOUR Problem
Mathway requires javascript and a modern browser.