if the legs of a right triangle have length of 6 in and 8 in what is the length of the hypotenuse
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
In this case, the lengths of the legs are 6 inches and 8 inches. Let's denote the length of the hypotenuse as c.
According to the Pythagorean theorem: c^2 = a^2 + b^2
Substituting the given values:
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
To find the length of the hypotenuse, we take the square root of both sides of the equation:
√c^2 = √100
c = 10
Therefore, the length of the hypotenuse is 10 inches.