Trigonometry Examples

Solve the Triangle tri{33.2}{}{}{61}{}{90}
Step 1
Find the last angle of the triangle.
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Step 1.1
The sum of all the angles in a triangle is degrees.
Step 1.2
Solve the equation for .
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Step 1.2.1
Add and .
Step 1.2.2
Move all terms not containing to the right side of the equation.
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Step 1.2.2.1
Subtract from both sides of the equation.
Step 1.2.2.2
Subtract from .
Step 2
Find .
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Step 2.1
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse.
Step 2.2
Substitute the name of each side into the definition of the sine function.
Step 2.3
Set up the equation to solve for the hypotenuse, in this case .
Step 2.4
Substitute the values of each variable into the formula for sine.
Step 2.5
Divide by .
Step 3
Find the last side of the triangle using the Pythagorean theorem.
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Step 3.1
Use the Pythagorean theorem to find the unknown side. In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (the two sides other than the hypotenuse).
Step 3.2
Solve the equation for .
Step 3.3
Substitute the actual values into the equation.
Step 3.4
Raise to the power of .
Step 3.5
Raise to the power of .
Step 3.6
Multiply by .
Step 3.7
Subtract from .
Step 4
Convert to a decimal.
Step 5
These are the results for all angles and sides for the given triangle.