The hypotenuse of a right triangle is the longest side, always opposite the right angle. There are two main methods to find the hypotenuse, depending on the information you have about the other sides:

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1. Using the Pythagorean Theorem:

This is the most common method and applies to any right triangle. The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Here's the formula:

c² = a² + b²

Steps to find the hypotenuse:

Identify the lengths of the other two sides (a and b). These can be given in the problem or you might need to find them using other formulas.

Square each side length (a² and b²).

Add the squares together (a² + b²).

Take the square root of the sum (√(a² + b²)) to find the length of the hypotenuse (c).

2. Using special right triangle properties:

For specific right triangles, like isosceles right triangles (where the two non-hypotenuse sides are equal), you can use their properties to find the hypotenuse without the Pythagorean theorem.

For example, in a 30-60-90 triangle, the hypotenuse is always

3

times the length of the shorter leg and twice the length of the longer leg.

Remember:

Make sure you are dealing with a right triangle before using either method.

The letters (a, b, and c) in the formula can represent any of the sides, but it's common practice to use c for the hypotenuse.

If you have a specific problem you're working on, feel free to share it, and I can help you find the hypotenuse.

This is the most common method and applies to any right triangle. The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

Here's the formula:

c² = a² + b²

Steps to find the hypotenuse:

Identify the lengths of the other two sides (a and b). These can be given in the problem or you might need to find them using other formulas.

Square each side length (a² and b²).

Add the squares together (a² + b²).

Take the square root of the sum (√(a² + b²)) to find the length of the hypotenuse (c).

2. Using special right triangle properties:

For specific right triangles, like isosceles right triangles (where the two non-hypotenuse sides are equal), you can use their properties to find the hypotenuse without the Pythagorean theorem.

For example, in a 30-60-90 triangle, the hypotenuse is always

3

times the length of the shorter leg and twice the length of the longer leg.

Remember:

Make sure you are dealing with a right triangle before using either method.

The letters (a, b, and c) in the formula can represent any of the sides, but it's common practice to use c for the hypotenuse.

If you have a specific problem you're working on, feel free to share it, and I can help you find the hypotenuse.