Which is the correct ratio of sides for a 30-60-90 triangle
-220 - 16 x 32
1:√3:2
The correct ratio of sides for a 30-60-90 triangle is often represented as 1 : √3 : 2. In this triangle, the angles measure 30 degrees, 60 degrees, and 90 degrees, respectively.
To understand how to obtain this ratio, let's consider the following steps:
1. Start with an equilateral triangle: Begin with an equilateral triangle in which all three sides are equal and all three angles are 60 degrees.
2. Divide the equilateral triangle: Draw an altitude from one vertex to the opposite side, creating a right triangle. The altitude divides the equilateral triangle into two congruent 30-60-90 triangles.
3. Determine the ratios: The ratio of the short leg to the hypotenuse in a 30-60-90 triangle is 1 : 2. Additionally, the ratio of the long leg to the hypotenuse is √3 : 2.
Therefore, the correct ratio of sides for a 30-60-90 triangle is 1 : √3 : 2.