Trigonometry Examples

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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.
Substitute the known values into the law of sines to find .
Solve the equation for .
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Evaluate .
Simplify .
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Simplify the numerator.
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Factor out of .
Apply the sine double-angle identity.
Evaluate .
Evaluate .
Simplify the numerator.
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Multiply by .
Multiply by .
Divide by .
Simplify .
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Evaluate .
Divide by .
Evaluate .
Solve for .
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Multiply each term by and simplify.
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Multiply each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Cancel the common factor of .
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Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
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Multiply and .
Divide by .
Multiply by .
Rewrite the equation as .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
Divide by .
The sum of all the angles in a triangle is degrees.
Solve the equation for .
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Add and .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from .
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.
Substitute the known values into the law of sines to find .
Solve the equation for .
Tap for more steps...
Evaluate .
Simplify .
Tap for more steps...
Evaluate .
Divide by .
Simplify .
Tap for more steps...
Evaluate .
Divide by .
Evaluate .
Solve for .
Tap for more steps...
Multiply each term by and simplify.
Tap for more steps...
Multiply each term in by .
Simplify the left side of the equation by cancelling the common factors.
Tap for more steps...
Cancel the common factor of .
Tap for more steps...
Write as a fraction with denominator .
Factor out the greatest common factor .
Cancel the common factor.
Rewrite the expression.
Simplify.
Tap for more steps...
Multiply and .
Divide by .
Multiply by .
Rewrite the equation as .
Divide each term by and simplify.
Tap for more steps...
Divide each term in by .
Cancel the common factor of .
Divide by .
These are the results for all angles and sides for the given triangle.
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