A 90-60-30 triangle is a special type of right triangle that has two angles that measure 90 degrees and 60 degrees. The side opposite the 90-degree angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called the legs of the triangle.
To find the sides of a 90-60-30 triangle, you can use the Pythagorean theorem and the ratios of the sides. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a 90-60-30 triangle, the ratio of the sides is 1:√3:2. This means that if you know the length of one side, you can find the lengths of the other two sides using the following formulas:
If you know the length of the hypotenuse (the longest side), you can find the lengths of the other two sides using the following formulas:
Leg A = hypotenuse / 2
Leg B = hypotenuse * √3 / 2
If you know the length of Leg A, you can find the lengths of the other two sides using the following formulas:
Leg B = Leg A * √3
Hypotenuse = 2 * Leg A
If you know the length of Leg B, you can find the lengths of the other two sides using the following formulas:
Leg A = Leg B / √3
Hypotenuse = 2 * Leg B / √3
For example, if you know that the hypotenuse is 10, you can find the lengths of the other two sides as follows:
Leg A = 10 / 2 = 5
Leg B = 10 * √3 / 2 = 5 * 1.732 = 8.66
Therefore, the sides of a 90-60-30 triangle with a hypotenuse of 10 are 5, 8.66, and 10.