What s the length of the hypotenuse in a right triangle with sides lengths of 8 and 15

17 units

Step-by-step explanation:

Pythagorean Theorem:

Where a and b are side lengths and c is the hypotenuse

Substitute:

Solve:

Add:

Find the square root:

17 = c

Therefore, the length of the hypotenuse is 17 units.

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse, or a² + b² = c². The legs, a and b, are the perpendicular sides to the right triangle and the hypotenuse, c, is the side opposite the right angle.

Since we have a right triangle, we can use the pythagorean theorem.

So here, since our legs have lengths of 8 and 15, and our hypotenuse has a length of x, we can set up the equation (8)² + (15)² = (x)².

Solving from herem (8)² is 8 · 8 or 64 and (15)² is 15 · 15 or 225.

So we have 64 + 225 = x².

64 + 225 is 289 so we have 289 = x².

Now to get x by itself, since x is being squared, we must take the square root of x and if we take the square root of the right side

of the equation, we must also take the square root

of the left side of the equation.

On the left, the square root of 289 is 17 and on the right, the square root of x² is x. So our answer is 17 = x.

step-by-step explanation: