How to Find the Length of the Leg in a Right Triangle using Pythagorean Theorem

Leg of a Right Triangle

A side adjacent to the right angle in a right triangle

In a right triangle, the leg refers to one of the two sides that form the right angle. The other side that forms the right angle is called the base. The leg that is opposite the angle that is not the right angle is called the opposite leg, while the leg that is adjacent to the angle that is not the right angle is called the adjacent leg.

It’s important to note that the Pythagorean theorem can be used to find the length of the leg of a right triangle. The Pythagorean theorem states that the square of the hypotenuse (longest side of a right triangle) is equal to the sum of the squares of the legs. Therefore, to find the length of a leg, we can use the formula:

a = √(c² – b²)

where a is the leg we want to find, c is the hypotenuse, and b is the other leg.

For example, if we have a right triangle with a hypotenuse of 10 and one leg of 6, we can find the length of the other leg as follows:

a = √(c² – b²)
a = √(10² – 6²)
a = √(100 – 36)
a = √64
a = 8

Therefore, the length of the other leg is 8.

In summary, a leg is one of the two sides that form a right angle in a right triangle, and we can use the Pythagorean theorem to find its length.

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