Hypotenuse – Examples and Practice Problems

What is Hypotenuse?

Hypotenuse – Examples: The length of the hypotenuse of a right triangle is the longest side and is always the side opposite the right angle.

Applications of the Hypotenuse

• There are many applications of the hypotenuse in mathematics and beyond. Some of the most common applications include finding the length of a side of a right triangle, finding the hypotenuse of a triangle, and using the Pythagorean theorem.
• In geometry, the length of a side of a right triangle can be found by using the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse. This theorem can be used to find the length of the hypotenuse of a triangle, or to find the length of a side of a triangle if two of the sides are known.
• The hypotenuse can also be used in trigonometry. In particular, the hypotenuse is used in the sine and cosine functions. These functions can be used to find the angles of a triangle, or to find the length of a side of a triangle if two of the angles are known.

Find The Hypotenuse, Opposite, and Adjacent

• There are a few different ways to find the hypotenuse, opposite, and adjacent of a right triangle. One way is to use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse. Another way is to use the trigonometric functions of sine, cosine, and tangent.
• The Pythagorean theorem can be used to find the length of the hypotenuse, opposite, and adjacent of a right triangle. The theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse. This theorem can be used to find the length of the hypotenuse, opposite, and adjacent of a right triangle if the lengths of the two shorter sides are known.
• The trigonometric functions of sine, cosine, and tangent can also be used to find the length of the hypotenuse, opposite, and adjacent of a right triangle. These functions can be used to find the length of the hypotenuse, opposite, and adjacent of a right triangle if the angles of the triangle are known.

Find the Length of the Hypotenuse

we will be finding the length of the hypotenuse of a right triangle. We will be using the Pythagorean theorem to do so.

The Pythagorean theorem states that the length of the hypotenuse of a right triangle is equal to the sum of the lengths of the other two sides squared. In this problem, we will be using the lengths of the other two sides to find the length of the hypotenuse.

The length of the first side is 9 units, and the length of the second side is 10 units. To find the length of the hypotenuse, we will square the length of the first side and add it to the square of the length of the second side.

9^2 + 10^2 = 100

The length of the hypotenuse is 10 units.

Calculate Hypotenuse from the Sides

• The hypotenuse of a right triangle is the side opposite the right angle.
• To calculate the hypotenuse, use the Pythagorean theorem.
• The Pythagorean theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.

Calculate Hypotenuse from an Angle and a Side

The hypotenuse is the longest side of a right triangle. To calculate it, use the Pythagorean theorem, which states that the length of the hypotenuse is the square root of the sum of the squares of the other two sides.

To find the hypotenuse of a right triangle, enter the values for the angle and the length of the adjacent side into the Pythagorean theorem equation:

h = √(x² + y²)