Understanding Right Triangles | Geometry, Trigonometry & Pythagorean Theorem

right triangle

A right triangle is a geometric shape that consists of three sides and three angles

A right triangle is a geometric shape that consists of three sides and three angles. It is called a “right” triangle because one of its angles is a right angle, which measures exactly 90 degrees (denoted by the symbol ⊾).

In a right triangle, the side opposite the right angle is called the hypotenuse, and it is the longest side. The other two sides are called the legs of the triangle. One leg is adjacent to the acute angle opposite it, while the other leg is opposite that angle.

The relationship between the sides of a right triangle is governed by the Pythagorean theorem. This theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):

c^2 = a^2 + b^2

This theorem is extremely useful in solving various problems related to right triangles. By knowing the lengths of two sides, you can calculate the length of the third side.

Additionally, right triangles have various trigonometric functions associated with their angles. The three main trigonometric functions are sine, cosine, and tangent. These functions relate the ratios of the sides of a right triangle to the angles formed by those sides. They can be used to solve problems involving angles and distances within right triangles.

Overall, right triangles play a significant role in geometry and trigonometry, as they provide a foundation for understanding various geometric concepts and mathematical relationships.

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