In any triangle, the angle measures add up to 180º.Here are a few triangle properties to be aware of: How do we know that the side lengths of the 30-60-90 triangle are always in the ratio 1 : 3–√ : 2 ? While we can use a geometric proof, it’s probably more helpful to review triangle properties, since knowing these properties will help you with other geometry and trigonometry problems. You can find the long leg by multiplying the short leg by the square root of 3. The length of the hypotenuse is always two times the length of the shortest leg. The shortest leg is across from the 30-degree angle. In any 30-60-90 triangle, you see the following: If you look at the 30–60–90-degree triangle in radians, it translates to the following: Two of the most common right triangles are 30-60-90 and 45-45-90 degree triangles. Because it is a special triangle, it also has side length values which are always in a consistent relationship with one another.Īll 30-60-90-degree triangles have sides with the same basic ratio. 30 60 90 Triangle RatioĪ 30-60-90 triangle is a special right triangle (a right triangle being any triangle that contains a 90 degree angle) that always has degree angles of 30 degrees, 60 degrees, and 90 degrees. This allows lines of, ,, and to be drawn by sliding the drafting triangle along a T-square. comm., Aug. 25, 2010 OEIS A180308).ģ0-60-90 triangles are used in drafting, as illustrated above. (E. Weisstein, M. Trott, A. Strzebonski, pers.