Pythagorean Theorem - In any right triangle, the sum of the squares of the legs equals the square of the hypotenuse

Proof of Pythagorean Theorem

Pythagorean Triple - A set of positive intergers a, b, and c that satisfy the equation c^2=a^2 + b^2. For example the integers 3, 4, and 5 form a Pythagorean Triple because 5^2 = 3^2 + 4^2.

Problems

Using the Pythagorean Theorem to find unknown parts of a right triangle.

1. Given the following right triangle, what is the length of side x as well as the length of the sides of the triangle?

2. In slow-pitch softball, the distance between consecutive bases is 65 feet. The pitcher's plate is located on a line between second base and home plate, 50 feet from home plate. How far is the pitcher's plate from second base?

65^2 + 65^2 = hypotenuse^2

4225 + 4225 = 8450

The square root of 8450 is approximately 91.9. So 91.9ft - 50ft = 41.9ft

The pitchers plate is approximately 41.9 feet from second base.

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