How to Find Angles in an Isosceles Triangle for High School Geometry
For a triangle to be an isosceles triangle, two of its three sides must be the same length. Because the two equal sides intersect identically with the third side, two of the triangle's angles also have the same measurement. Through the law of cosines, which is a trigonometric property that relates the measurement of a triangle's angle through the lengths of its sides, you can find the angles of an isosceles triangle in your high school geometry class.
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Instructions
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Square the length of each of its sides. For this example, the sides measure 10, 10 and 15. The square of 10 is 100, and the square of 15 is 225.
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Add the squares of the same length sides together, and then subtract the square of the third side from the sum. For this example, 100 added to 100 is 200, and 200 less 225 is -25.
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Divide the amount calculated in the previous step by the squares of one of the equal sides doubled. For this example, 100 multiplied by 2 is 200, and -25 divided by 200 results in -0.125.
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Find the arccosine of the number calculated in the previous step. The arccosine is an inverse trigonometric function, and will be labeled on a scientific calculator as "arccos" or "cos^-1." For this example, the arccosine of -0.125 is 97.180756 degrees. This is the measurement of the unequal angle.
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Subtract the angle calculated in the previous step from 180, and then halve the difference to find the measurement of the two equal angles. For this example, 180 less 97.180756 results in 82.819244, and half of 82.819244 is 41.409622. The triangle's angles measure 97.180756, 41.409622 and 41.409622 degrees.
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