How to Find the Side Length of a Right Triangle
Working with the sides and angles of a triangle are a large part of learning math and geometry. A right triangle is one that has an angle of 90 degrees, meaning the two shorter sides are perpendicular to each other. If a triangle is a right triangle, and you know the length of two of the sides, you can use the Pythagorean theorem to figure out the length of the missing side.
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Instructions
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Determine if you can find the length of the missing side with the triangle you are using. The triangle must be a right triangle (a triangle with one angle equaling 90 degrees), and you must know the length of two of the sides to use the Pythagorean theorem. If these things are not true, you will not be able to use this method.
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Write down the theorem. It states that the sum of the squares of the two shorter sides of a right triangle are equal to the square of the longer side. The equation is written as a² + b² = c², with a and b being the shorter sides and c being the longest.
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Fill in the information you know into the equation. Plug in the sides you know into the corresponding letters of the equation. The c value will always correspond to the largest side, but if you know the length of a shorter side, you can substitute it for either a or b.
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Square the numbers that you do know to get rid of the exponents. Then subtract the value you know from the left side of the equation from the right side. For example, if the equation is 2² + b² = 5², you will square both 2 and 5 to get 4 + b² = 25. Subtract 4 from both sides to bet b² = 21.
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Calculate the square root of the number on the right side of the equation to determine the length of the missing side. Use a calculator since the answer will most likely not be a whole number. The result will be your answer. Using the example of b² = 21, you will determine the square root of both sides to get b = 4.58257569.
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