The ratio between the base, the height, and the hypotenuse of this triangle is 1: 1: √2.īase: Height: Hypotenuse = x: x: x√2 = 1: 1: √2 This special right triangle has angles measuring 45°, 45°, and 90°. The Two Main Types of Special Right Triangles are Thus, the area of a special right triangle is one-half the product of the legs’ lengths. Another important characteristic of special right triangles is that their legs are also the altitudes of the triangles.The sides of these special right triangles are in particular ratios known as Pythagorean triples.It rapidly reproduces the values of trigonometric functions for the angles 30°, 45°, and 60°. We can deduce the side lengths from the basis of the unit circle or other geometric methods.These two triangles are also similar to the main triangle. The altitude of a triangle arising from the right angle to the hypotenuse equally divides the main triangle into two similar triangles. ![]() It is the longest side of the right-angle triangle. The side opposite to the right angle is the hypotenuse.The largest angle of the triangle is equal to the sum of the other two angles.Special right triangles are angle-based, i.e., they are specified by the relationships of their angles. Length of a leg a 2 = c 2 – b 2, where c is the hypotenuse length, and b is the length of the other leg. Length of hypotenuse c 2 = a 2 + b 2, where a and b are the lengths of the triangle legs. If we know the relationships of the angles or ratios of sides of special right triangles, we can quickly calculate various lengths without having to resort to advanced methods. , or of other special numbers such as the golden ratio. On the other hand, a “side-based” right triangle has lengths of the sides forming ratios of whole numbers- 3: 4: 5. ![]() For instance, a right triangle with angles forming simple relationships, such as 45°–45°–90°, is an “angle-based” right triangle.
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