The side ration of a 30-60-90 triangle is …
The side ratio of a 30-60-90 triangle is commonly represented as 1:√3:2
The side ratio of a 30-60-90 triangle is commonly represented as 1:√3:2.
In a 30-60-90 triangle, the angles measure 30 degrees, 60 degrees, and 90 degrees, respectively. The longest side, opposite the right angle, is known as the hypotenuse. Let’s assume the length of the shorter leg (opposite the 30-degree angle) is x and the length of the longer leg (opposite the 60-degree angle) is y.
To find the side ratio of this triangle, we need to determine the relationship between the lengths of the sides.
In a 30-60-90 triangle, we use the ratios derived from the properties of special right triangles. The ratios are as follows:
Shorter leg (opposite 30 degrees) = x
Longer leg (opposite 60 degrees) = y
Hypotenuse (opposite 90 degrees) = 2x
Using trigonometry, we can determine the lengths of the sides:
The sine of 30 degrees is defined as the ratio of the length of the opposite side to the hypotenuse: sin(30) = x / (2x) = 1/2.
This implies x = (1/2) * (2x) = x.
The sine of 60 degrees is defined as the ratio of the length of the opposite side to the hypotenuse: sin(60) = y / (2x) = √3/2.
This implies y = (√3/2) * (2x) = √3x.
Therefore, the side ratio of a 30-60-90 triangle is x : √3x : 2x, which can be simplified as 1 : √3 : 2.
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