30-60-90 triangle
A 30-60-90 triangle is a special type of right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees
A 30-60-90 triangle is a special type of right triangle where the angles measure 30 degrees, 60 degrees, and 90 degrees. The sides of this triangle have a specific relationship to one another. Let’s denote the lengths of the sides as follows:
– Let’s call the side opposite the 30-degree angle as “a.”
– The side opposite the 60-degree angle can be denoted as “b.”
– The side opposite the 90-degree angle is the hypotenuse and can be represented as “c.”
The relationship between these side lengths in a 30-60-90 triangle is as follows:
1. The side opposite the 30-degree angle (a) is half the length of the hypotenuse (c). So, a = (1/2) * c.
2. The side opposite the 60-degree angle (b) is found by multiplying the length of the side opposite the 30-degree angle (a) by the square root of 3. So, b = a * √3.
3. Finally, the ratio of the lengths of the sides in a 30-60-90 triangle is: a : b : c = 1 : √3 : 2.
It’s important to note that these ratios only hold true for 30-60-90 triangles. If you have one side length given in a triangle and it fits the 30-60-90 angle measurements, you can use these ratios to find the other side lengths.
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