Master The Fundamentals: Right Triangles, Pythagorean Theorem, And Special Ratios

Right Triangle

a triangle with one right angle

A right triangle is a type of triangle that has one angle measuring 90 degrees or, in other words, one angle that is a right angle. In a right triangle, the side opposite to the right angle is called the hypotenuse, while the other two sides are called the legs. The hypotenuse is always the longest side of the triangle.

The Pythagorean Theorem is a formula used to find the length of one of the sides of a right triangle, given the lengths of the other two sides. The formula states that the square of the length of the hypotenuse is equal to the sum of the squares of the length of the other two sides. In other words, a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Special right triangles are right triangles that have some special ratios and properties that can make them easier to solve. There are two types of special right triangles: the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, each of the two legs is congruent, and the length of the hypotenuse is equal to the length of a leg times the square root of 2. In a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the shorter leg times the square root of 3.

Right triangles are used in various applications of mathematics and other fields, such as physics, engineering, and architecture. The properties and formulas associated with right triangles make them a fundamental concept to understand for students of mathematics and science.

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