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.
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