Some Specific Examples. Note: The hypotenuse is the longest side in a right triangle, which is different from the long leg. If you look at the 30–60–90-degree triangle in radians, it translates to the following: In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle. The long leg is the leg opposite the 60-degree angle. Special right triangles such as the 30-60-90 triangle and the 45-45-90 triangles have a formula for the value of the sides. Find out what are the sides, hypotenuse, area and perimeter of your shape and learn about 45 45 90 triangle formula, ratio and rules. In a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : . Solution: As it is a right triangle in which the hypotenuse is the double of one of the sides of the triangle. They are special because, with simple geometry, we can know the ratios of their sides. Practice Using Special Right Triangles. We will prove that below. Thus, it is called a 30-60-90 triangle where smaller angle will be 30. THE 30°-60°-90° TRIANGLE. Example 1: Find the missing side of the given triangle. Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles.All 30-60-90 triangles, have sides with the same basic ratio.If you look at the 30–60–90-degree triangle in radians, it translates to the following: (Don't use the Pythagorean theorem. The other is the isosceles right triangle. All 30-60-90-degree triangles have sides with the same basic ratio. One is the 30°-60°-90° triangle. Theorem. Problem 1. 45, 45, 90 Special Right Triangle. The picture below illustrates the general formula for the 30, 60, 90 Triangle. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b = asin(60 degrees)=1/2asqrt(3) (1) c = asin(30 degrees)=1/2a, (2) and the area is A=1/2bc=1/8sqrt(3)a^2. Specific Examples. General Formula. Two of the most common right triangles are 30-60-90 and the 45-45-90 degree triangles. What is the value of z in the triangle below? If you want to know more about another popular right triangles, check out this 30 60 90 triangle tool and the calculator for special right triangles. Definitions and formulas for the area of a triangle, the sum of the angles of a triangle, the Pythagorean theorem, Pythagorean triples and special triangles (the 30-60-90 triangle and the 45-45-90 triangle) Just scroll down or click on what you want and I'll scroll down for you! Use the properties of special right triangles described on this page) Show Answer. THERE ARE TWO special triangles in trigonometry. A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. Example of 30 – 60 -90 rule. (3) The inradius r and circumradius R are r = 1/4(sqrt(3)-1)a (4) R = 1/2a.