Trigonometry Examples

Solve the Triangle A=67 , a=11 , b=24
, ,
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
Multiply both sides of the equation by .
Step 3.2
Simplify both sides of the equation.
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Step 3.2.1
Simplify the left side.
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Step 3.2.1.1
Cancel the common factor of .
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Step 3.2.1.1.1
Cancel the common factor.
Step 3.2.1.1.2
Rewrite the expression.
Step 3.2.2
Simplify the right side.
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Step 3.2.2.1
Simplify .
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Step 3.2.2.1.1
Evaluate .
Step 3.2.2.1.2
Divide by .
Step 3.2.2.1.3
Multiply by .
Step 3.3
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 4
There are not enough parameters given to solve the triangle.
Unknown triangle
Step 5
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 6
Substitute the known values into the law of sines to find .
Step 7
Solve the equation for .
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Step 7.1
Multiply both sides of the equation by .
Step 7.2
Simplify both sides of the equation.
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Step 7.2.1
Simplify the left side.
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Step 7.2.1.1
Cancel the common factor of .
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Step 7.2.1.1.1
Cancel the common factor.
Step 7.2.1.1.2
Rewrite the expression.
Step 7.2.2
Simplify the right side.
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Step 7.2.2.1
Simplify .
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Step 7.2.2.1.1
Evaluate .
Step 7.2.2.1.2
Divide by .
Step 7.2.2.1.3
Multiply by .
Step 7.3
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 8
There are not enough parameters given to solve the triangle.
Unknown triangle
Step 9
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 10
Substitute the known values into the law of sines to find .
Step 11
Solve the equation for .
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Step 11.1
Multiply both sides of the equation by .
Step 11.2
Simplify both sides of the equation.
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Step 11.2.1
Simplify the left side.
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Step 11.2.1.1
Cancel the common factor of .
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Step 11.2.1.1.1
Cancel the common factor.
Step 11.2.1.1.2
Rewrite the expression.
Step 11.2.2
Simplify the right side.
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Step 11.2.2.1
Simplify .
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Step 11.2.2.1.1
Evaluate .
Step 11.2.2.1.2
Divide by .
Step 11.2.2.1.3
Multiply by .
Step 11.3
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 12
There are not enough parameters given to solve the triangle.
Unknown triangle
Step 13
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 14
Substitute the known values into the law of sines to find .
Step 15
Solve the equation for .
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Step 15.1
Multiply both sides of the equation by .
Step 15.2
Simplify both sides of the equation.
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Step 15.2.1
Simplify the left side.
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Step 15.2.1.1
Cancel the common factor of .
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Step 15.2.1.1.1
Cancel the common factor.
Step 15.2.1.1.2
Rewrite the expression.
Step 15.2.2
Simplify the right side.
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Step 15.2.2.1
Simplify .
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Step 15.2.2.1.1
Evaluate .
Step 15.2.2.1.2
Divide by .
Step 15.2.2.1.3
Multiply by .
Step 15.3
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 16
There are not enough parameters given to solve the triangle.
Unknown triangle
Step 17
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 18
Substitute the known values into the law of sines to find .
Step 19
Solve the equation for .
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Step 19.1
Multiply both sides of the equation by .
Step 19.2
Simplify both sides of the equation.
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Step 19.2.1
Simplify the left side.
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Step 19.2.1.1
Cancel the common factor of .
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Step 19.2.1.1.1
Cancel the common factor.
Step 19.2.1.1.2
Rewrite the expression.
Step 19.2.2
Simplify the right side.
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Step 19.2.2.1
Simplify .
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Step 19.2.2.1.1
Evaluate .
Step 19.2.2.1.2
Divide by .
Step 19.2.2.1.3
Multiply by .
Step 19.3
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 20
There are not enough parameters given to solve the triangle.
Unknown triangle
Step 21
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 22
Substitute the known values into the law of sines to find .
Step 23
Solve the equation for .
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Step 23.1
Multiply both sides of the equation by .
Step 23.2
Simplify both sides of the equation.
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Step 23.2.1
Simplify the left side.
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Step 23.2.1.1
Cancel the common factor of .
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Step 23.2.1.1.1
Cancel the common factor.
Step 23.2.1.1.2
Rewrite the expression.
Step 23.2.2
Simplify the right side.
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Step 23.2.2.1
Simplify .
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Step 23.2.2.1.1
Evaluate .
Step 23.2.2.1.2
Divide by .
Step 23.2.2.1.3
Multiply by .
Step 23.3
The range of sine is . Since does not fall in this range, there is no solution.
No solution
No solution
Step 24
There are not enough parameters given to solve the triangle.
Unknown triangle