In a right-angled triangle, the height is the perpendicular of the triangle.

The formula to calculate the area of a triangle is = (1/2) × base × height. These sides also follow the same ratio a/2 : (a√3)/2: a Hence, we can apply the Pythagoras theorem to find the length AD. Both the triangles are similar and right-angled triangles. Triangle ABD and ADC are two 30-60-90 triangles. The perpendicular in an equilateral triangle bisects the other side. Now, draw a perpendicular from vertex A to side BC at point D of the triangle ABC. Let's consider an equilateral triangle ABC with a side length equal to 'a'. Another formula for this special triangle 1:2:3 which is the ratio of the three angles of the 30-60-90-Triangle. The above theorem can be written mathematically as the 30-60-90-Triangle Formula as 1:√3: 2 which is the ratio of the three sides of the 30-60-90-Triangle. Statement: The length of the hypotenuse is twice the length of the shortest side and the length of the other side is √3 times the length of the shortest side in a 30-60-90-Triangle.

The statement of the 30-60-90-Triangle Theorem is given as, The side opposite to the 90° angle, the hypotenuse AC = 2y = 2 × 7 = 14.The side opposite to the 60° angle, BC = y √3 = 7 √3.The side opposite to the 30° angle, AB = y = 7.The side opposite to the 90° angle, the hypotenuse AC = 2y = 2 × 2 = 4.The side opposite to the 60° angle, BC = y √3 = 2 √3.The side opposite to the 30° angle, DE = y = 2.This formula can be verified using the Pythagoras theorem.Ĭonsider some of the examples of a 30-60-90 degree triangle with these side lengths: Let us learn the derivation of this ratio in the 30-60-90 triangle proof section. This is also known as the 30-60-90 triangle formula for sides y: y√3: 2y. The sides of a 30-60-90 triangle are always in the ratio of 1:√3: 2. On the side that is opposite to the 90° angle, the hypotenuse AC = 2y will be the largest side because 90° is the largest angle.The side that is opposite to the 60° angle, BC = y × √3 = y √3 will be the medium length because 60° is the mid-sized degree angle in this triangle.The side that is opposite to the 30° angle, AB = y will always be the smallest since 30° is the smallest angle in this triangle.We can understand the relationship between each of the sides from the below definitions: A 30-60-90 triangle is a special triangle since the length of its sides is always in a consistent relationship with one another.

Formula for isosceles right triangle