# What is a hypotenuse in a triangle?

## What is a hypotenuse in a 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. The hypotenuse of a right triangle is always the side opposite the right angle.

How do you label the legs and hypotenuse of a triangle?

Summary

1. The legs are the shorter sides and meet at the right angle.
2. The hypotenuse is the longest side and is across from the right angle.
3. In the Pythagorean Theorem, it doesn’t matter which leg you label a and which leg you label b.
4. BUT the hypotenuse must always be labeled c.

### How do you find hypotenuse?

The hypotenuse is termed as the longest side of a right-angled triangle. To find the longest side we use the hypotenuse formula that can be easily driven from the Pythagoras theorem, (Hypotenuse)2 = (Base)2 + (Altitude)2. Hypotenuse formula = √((base)2 + (height)2) (or) c = √(a2 + b2).

How do I find the hypotenuse of a triangle?

Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²)

#### Which letter is the hypotenuse?

The lowercase letters c, a, and b are used to represent the lengths of the sides of the right triangle. The label of a vertex and the label of the opposite side correspond. So the side opposite the right angle C is labeled c; this special side is called the hypotenuse of the right triangle.

How do you find the sides of a triangle with hypotenuse?

If you have the hypotenuse, multiply it by sin(θ) to get the length of the side opposite to the angle. Alternatively, multiply the hypotenuse by cos(θ) to get the side adjacent to the angle.

## How to calculate hypotenuse angle?

The formula to find the hypotenuse is given by the square root of the sum of squares of base and perpendicular of a right-angled triangle . The hypotenuse formula can be expressed as; Hypotenuse = √ [Base2 + Perpendicular2] Let a, b and c be the sides of the triangle as per given figure below;

What is adjacent over a hypotenuse?

Cosine is the adjacent side over the hypotenuse (CAH), and sine is the opposite side over the hypotenuse (SOH). But the side adjacent to angle A is the same thing as the side opposite angle B.

### Is the hypotenuse always longest?

The square of the hypotenuse which is equal to the addition of the square of other two sides of the triangle. c2 =a2 + b2. The side which is opposite to that of the right angle 90° is called as the hypotenuse. This is always the longest side of the triangle.

What is the hypotenuse theorem?

The Hypotenuse Angle Theorem states that if one of the acute angles and the hypotenuse of a right triangle are congruent to the corresponding acute angle and hypotenuse of a second triangle, \his proves that the two triangles are also congruent. In math, this theorem is one of a few theorems used…

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