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How to Solve Pythagorean Problems

The Pythagorean theorem is a mathematical theorem that originated in ancient times under the inspiration and study of a Greek philosopher and mathematician named Pythagoras. The Pythagorean theorem is still used today to find the lengths of legs belonging to a right triangle, which is a triangle that possesses a 90 degree angle. You can solve Pythagorean problems by applying the simple formula "a^2 + b^2 = c^2." You most likely will run into Pythagorean problems in high school or college math courses.

Instructions

    • 1

      Observe the parts of a 90-degree triangle. The side that is opposite the 90-degree angle is known as the hypotenuse. The other two sides are known as legs. The hypotenuse is longer than either of the legs.

    • 2

      Find the length of the hypotenuse by measuring the length of each leg. Square the two legs by multiplying the length of each leg times itself. Then add the squares and take the square root of the sum to find the length of the hypotenuse. For example, consider a triangle with one leg that is 3 inches long and another leg that is 4 inches. Square 3 to get 9 and 4 to get 16. Add 9 plus 16 to get 25. Take the square root of 25 by figuring out which number times itself equals 25. Since 5 times 5 equals 25, then 5 is the square root of 25 and the length of the hypotenuse.

    • 3

      Find the length of one leg by measuring the hypotenuse and the other leg. Square the hypotenuse and the leg you measured. Then subtract the squared leg from the squared hypotenuse and take the square root of the difference to find the length of the other leg. For example, consider a triangle with a hypotenuse that is 10 inches long and one leg that is 6 inches long. Square 10 to get 100 and 6 to get 36. Subtract 36 from 100 to get 64. Take the square root of 64 to get 8, which is the length of the other leg.

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