Understanding the Hypotenuse | Definition, Pythagorean Theorem, and Trigonometry Applications in Geometry

Hypotenuse

The hypotenuse is a term used in geometry to refer to the longest side of a right-angled triangle

The hypotenuse is a term used in geometry to refer to the longest side of a right-angled triangle. It is also known as the “c” side, according to the Pythagorean theorem.

In a right-angled triangle, the hypotenuse is always opposite the right angle. It connects the two other sides of the triangle, known as the legs. The length of the hypotenuse is determined by the lengths of the two legs.

The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs. This can be written as:

c^2 = a^2 + b^2

where c represents the length of the hypotenuse, and a and b denote the lengths of the legs. This theorem allows us to find the length of the hypotenuse if we know the lengths of the other two sides, or vice versa.

The hypotenuse plays a significant role in trigonometry as well. In particular, the ratios of the sides of a right triangle, called trigonometric ratios (sine, cosine, and tangent), can be calculated using the lengths of the legs and the hypotenuse. These ratios are useful in various applications, such as solving for angles and distances in real-world scenarios.

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