A right triangle is a type of triangle that has one angle measuring exactly 90 degrees. This 90-degree angle, known as the right angle, is what gives the right triangle its name. The sides forming the right angle are called the ‘legs’, and the side opposite the right angle is the ‘hypotenuse’, which is always the longest side of the triangle.
Key Properties of Right Triangles
- One right angle: The defining feature of a right triangle is the presence of a 90-degree angle.
- The Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is expressed as a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.
- Trigonometric ratios: Right triangles are fundamental in trigonometry, as they allow for the definition of sine, cosine, and tangent functions.
Examples of Right Triangles
Example 1: In a triangle with sides measuring 3 cm, 4 cm, and 5 cm, the triangle is right-angled since 3^2 + 4^2 = 5^2 (9 + 16 = 25).
Example 2: A right triangle with a 30-degree angle and a 60-degree angle. The sides opposite these angles are in the ratio 1:√3:2.
Applications of Right Triangles
Right triangles have wide applications in geometry, engineering, architecture, and various fields that require calculation of heights and distances. They are integral in the study and application of trigonometry.
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