## right triangle

### A right triangle is a triangle that has one angle measuring 90 degrees (a right angle)

A right triangle is a triangle that has one angle measuring 90 degrees (a right angle). It is one of the basic shapes in geometry and is characterized by its unique properties.

In a right triangle, the side opposite the right angle is called the hypotenuse. The other two sides are referred to as the legs. The leg adjacent to a given angle is called the adjacent side, while the side opposite to the angle is called the opposite side.

One of the most famous theorems related to right triangles is the Pythagorean Theorem. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Mathematically, it can be expressed as:

c^2 = a^2 + b^2

Here, c represents the length of the hypotenuse, and a and b represent the lengths of the legs.

Right triangles have important applications in various fields of mathematics and physics. For instance, they are extensively used in trigonometry, which deals with the relationships between the angles and sides of triangles. Trigonometric ratios such as sine, cosine, and tangent are defined based on the ratios of the sides of right triangles.

In addition, the concept of similarity between triangles is often explored through the properties of right triangles. Right triangles can be used to find the heights of tall structures, determine distances, calculate angles and solve real-life problems involving measurements and distances.

Understanding right triangles and their properties is fundamental in many areas of math and can be applicable in practical situations.

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