The side ration of a 30-60-90 triangle is …
In a 30-60-90 triangle, the sides are in the ratio 1:√3:2
In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. This means that if the shortest side (opposite the 30-degree angle) is represented by the value x, then the side opposite the 60-degree angle is √3x, and the hypotenuse (opposite the 90-degree angle) is 2x.
To understand how this ratio is derived, consider the following diagram:
/
/ theta
x /__________
/
/
/
In the triangle above, theta (θ) represents the 30-degree angle. The side opposite θ has length x, and the side opposite the right angle has length 2x. By using trigonometric ratios, we can determine the length of the side opposite the 60-degree angle.
Using sine function: sin(θ) = opposite/hypotenuse, we get:
sin(30) = x/2x
1/2 = x/2x
1/2 = 1/2
Since sin(30) = 1/2, it means that x/2x = 1/2, which simplifies to x = 1.
So, in a 30-60-90 triangle, the sides are in the ratio 1:√3:2. Therefore, the side opposite the 30-degree angle has a length of 1, the side opposite the 60-degree angle has a length of √3, and the hypotenuse has a length of 2.
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