How to Find the Leg Size of Triangles
Triangles are geometric figures that have three sides and three angles. All of the interior angles of a triangle add up to 180 degrees. Triangles that have an interior angle equal to exactly 90 degrees are called right triangles, and the longest side of a triangle is called the hypotenuse. For these examples, the legs will be labeled "a" and "b," while the hypotenuse will be labeled "c." The Pythagorean theorem is one of the oldest mathematical theorems, and it can be used to find the leg size of right triangles when you know the length of the hypotenuse and one other leg.
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Instructions
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Square the length of leg "a." For example, a right triangle has one leg measuring 3 inches in length and the hypotenuse is 5 inches. Leg "a" is 3 inches, and 3 squared equals 9.
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Square the length of the hypotenuse. In our example, the hypotenuse is 5 inches and 5 squared is 25.
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Subtract the square of the length of leg a from the square of the hypotenuse. For example, 25 minus 9 equals 16. The difference equals the square of the unknown side.
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Find the square root of the the difference. In our example, the square root of 16 is 4. The length of the unknown leg of the triangle is 4 inches.
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Check your answer by replacing the variables in the formula a^2 + b^2 = c^2 with the actual lengths of each side. In our example, 3^2 + 4^2 = 5^2, which simplifies to 25 = 25 -- confirming that our answer is correct.
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Tips & Warnings
The Pythagorean theorem can be rearranged using algebra to solve for any side. The square of the length of side "a" is equal to the square of the hypotenuse minus the square of the length of side "b."
The Pythagorean theorem only works with right triangles. For triangles other than right triangles, use the law of sines or law of cosines to find the length of an unknown leg.
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