Trigonometry Examples

Solve the Triangle A=53 , B=23 , C=104 , a=29/8
, , ,
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 .
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Step 3.1
Factor each term.
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Step 3.1.1
Evaluate .
Step 3.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.1.3
Evaluate .
Step 3.1.4
Divide by .
Step 3.1.5
Combine and .
Step 3.1.6
Divide by .
Step 3.2
Find the LCD of the terms in the equation.
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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.
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Step 3.3.1
Multiply each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Rewrite the expression.
Step 3.4
Solve the equation.
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Step 3.4.1
Rewrite the equation as .
Step 3.4.2
Divide each term in by and simplify.
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Step 3.4.2.1
Divide each term in by .
Step 3.4.2.2
Simplify the left side.
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Step 3.4.2.2.1
Cancel the common factor of .
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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.
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Step 3.4.2.3.1
Divide by .
Step 4
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 5
Substitute the known values into the law of sines to find .
Step 6
Solve the equation for .
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Step 6.1
Factor each term.
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Step 6.1.1
Evaluate .
Step 6.1.2
Multiply the numerator by the reciprocal of the denominator.
Step 6.1.3
Evaluate .
Step 6.1.4
Divide by .
Step 6.1.5
Combine and .
Step 6.1.6
Divide by .
Step 6.2
Find the LCD of the terms in the equation.
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Step 6.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 6.2.2
The LCM of one and any expression is the expression.
Step 6.3
Multiply each term in by to eliminate the fractions.
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Step 6.3.1
Multiply each term in by .
Step 6.3.2
Simplify the left side.
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Step 6.3.2.1
Cancel the common factor of .
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Step 6.3.2.1.1
Cancel the common factor.
Step 6.3.2.1.2
Rewrite the expression.
Step 6.4
Solve the equation.
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Step 6.4.1
Rewrite the equation as .
Step 6.4.2
Divide each term in by and simplify.
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Step 6.4.2.1
Divide each term in by .
Step 6.4.2.2
Simplify the left side.
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Step 6.4.2.2.1
Cancel the common factor of .
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Step 6.4.2.2.1.1
Cancel the common factor.
Step 6.4.2.2.1.2
Divide by .
Step 6.4.2.3
Simplify the right side.
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Step 6.4.2.3.1
Divide by .
Step 7
These are the results for all angles and sides for the given triangle.