How to Calculate the Angle of a Triangle With Given Lengths
A triangle is a commonly encountered geometric object that has three points, or vertices, and three sides. The triangle has been well-studied over the years, with the first formula describing triangles developed in ancient Greece. One important geometric law for triangles is the law of cosines. This law allows you to calculate the angle between any two sides of a triangle if the lengths of the sides of a triangle are known. The law of cosines can be applied in a series of short steps.
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Instructions
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Determine the angle that you wish to determine. Take note of the side of the triangle immediately opposite that angle. Call that opposite side "c."
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Calculate the square of the lengths of the two remaining sides of the triangles and add the results. For example, if the lengths of the two sides are 5 and 7, the square of these numbers are 25 and 49, respectively. The sum of these numbers is 74. Call this result "A."
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Determine the square of the length of the opposite side of the triangle. Subtract this from result A. For example, if the length of the opposite side is 8, squaring this number yields 64. Subtracting this from 74 gives 10. Call this result "B."
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Determine the product of the length of the two remaining sides of the triangles, then multiply the result by 2. In the example used here, the length of the two remaining sides is 5 and 7, so the product of these numbers is 35. Multiplying this by 2 gives 70. Call this result "C."
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Divide result B by result C. In the example here, dividing 10 by 70 gives 0.70. Call this result "D."
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Determine the arccos of result "D." This can be done on a scientific calculator by pressing the "2nd" button, then pressing the "cos" button. The arccos of 0.70 is 81.8 degrees. This is the angle of one side of the triangle. The remaining two angles of the triangle can be found in a similar fashion.
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References
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