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Definitions from the Web

Term: Hypotenuse

Description:

The term "hypotenuse" refers to the longest side of a right-angled triangle, which is opposite to the right angle. It is responsible for connecting the two shorter sides of the triangle, known as the legs. The length of the hypotenuse can be determined using the Pythagorean theorem.

Senses:

Sense 1 (Mathematics):

In mathematics, the hypotenuse is a fundamental concept used in geometry, particularly in the study of right-angled triangles. It is essential for calculating various properties of triangles, such as their angles, side lengths, and areas.

Usages:

Usage 1 (Geometry):

In geometry, the hypotenuse is often used to determine the length of a side or an angle in a right-angled triangle. By applying the Pythagorean theorem, one can find the hypotenuse when the lengths of the two legs are known.

Usage 2 (Trigonometry):

Trigonometry extensively utilizes the concept of the hypotenuse. It is an important component in various trigonometric functions, such as sine, cosine, and tangent. These functions allow for the calculation of angles and side lengths in right-angled triangles.

Sample Sentences:

1. The length of the hypotenuse in this right triangle is 10 centimeters.

2. To find the angle of elevation, we need to know the length of the hypotenuse.

3. The formula to calculate the hypotenuse of a right triangle is c = √(a² + b²).

4. The hypotenuse of a 45-45-90 triangle is always sqrt(2) times the length of its legs.

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