Question

I need to understand this

Answer 1

So on a 30 degree 60 degree 90 degree triangle, the sides have a special relationship

so before we begin, just know that the square root of 3 is less than 2 (square root 3 is about 1.7). Even though it would seem like more than two, it isn't.

If we look at the triangle in the attached image, I show the relationships of the sides. The shortest side that is opposite of the 30 degree has a value of x, the second longest side opposite from the 60 degree has a value of square root 3 x, and the hypotenuse (the longest side) has a value of 2x. 

In your example, the second longest side has a value of 10 times the square root of 3. If we look at our ratio for that side, we see that it is square root 3 times x. Therefore, our "x" that will determine all sides is 10 in this triangle. 

If x = 10, then the shortest side is 10 (just x), the second longest is square root 3 times 10 (which is already given to us), and the hypotenuse is 2 times 10.

This concept is called a SPECIAL RIGHT TRIANGLE. In a 45-45-90 degree right triangle, the two shorter sides are equal and the hypotenuse is the length of one of the sides times the square root of three. In a 30-60-90 degree right triangle, the smallest side is x, the second largest is square root of 3 times x, and the hypotenuse or longest is 2x.