# What is the length of the hypotenuse if the legs are 6 and 8?

## What is the length of the hypotenuse if the legs are 6 and 8?

1 Expert Answer You require the Pythagorean Theorem: in a right triangle the sum of the squares of the legs equals the square of the hypotenuse. In this case 6^2 + 8^2 = 36 + 64 = 100 = 10^2, i.e. the hypotenuse is 10.

## What is the length of the hypotenuse of a triangle?

In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.

What is the shortest side of a 30 60 90 triangle?

And because we know that we cut the base of the equilateral triangle in half, we can see that the side opposite the 30° angle (the shortest side) of each of our 30-60-90 triangles is exactly half the length of the hypotenuse.

### What are the side lengths of a 45 45 90 triangle?

A 45°-45°-90° triangle is a special right triangle that has two 45-degree angles and one 90-degree angle. The side lengths of this triangle are in the ratio of; Side 1: Side 2: Hypotenuse = n: n: n√2 = 1:1: √2. The 45°-45°-90° right triangle is half of a square.

### What is the 30-60-90 triangle formula?

30°-60°-90° Triangles In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg. To see why this is so, note that by the Converse of the Pythagorean Theorem, these values make the triangle a right triangle.

What is the shortest side of a 30-60-90 triangle?

#### Is a right triangle A 9 B 12 C 15?

Correct answer: Explanation: By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

#### How do you find two legs of a right triangle?

Because you know both legs are equal, you know the length of both the legs. You can find the hypotenuse by multiplying this length by the square root of 2. Type 2: You’re given the hypotenuse. Divide the hypotenuse by the square root of 2 to find the legs (which are equal).

Is the hypotenuse the longest side of any triangle?

In a right triangle, the hypotenuse is the longest side, an “opposite” side is the one across from a given angle, and an “adjacent” side is next to a given angle. We use special words to describe the sides of right triangles. It is the longest side in a right triangle.