# How do you know when to use the special right triangles?

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Special right triangles, namely the 45-45-90 triangle and the 30-60-90 triangle, are used in geometry when dealing with right triangles that have specific angle measurements. You can recognize when to use these special triangles based on the given angles or side lengths in a problem.

In a 45-45-90 triangle, both acute angles are congruent, measuring 45 degrees each, and the lengths of the legs are equal. The hypotenuse is √2 times the length of either leg. This triangle is commonly used when working with squares, equilateral triangles, or regular polygons with interior angles measuring 45 degrees.

In a 30-60-90 triangle, the angles measure 30, 60, and 90 degrees. The side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is (√3)/2 times the length of the hypotenuse. This triangle is often used when working with hexagons, as well as when finding side lengths or angles in geometry problems involving equilateral triangles or regular polygons with interior angles measuring 60 degrees.

You may also recognize the need for special right triangles when solving problems involving trigonometric functions such as sine, cosine, and tangent, where the angles involved are multiples of 30 or 45 degrees.

In summary, special right triangles are used when dealing with specific angle measurements or side lengths in right triangles, particularly in geometry problems involving regular polygons or trigonometric functions.

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