Question

The shorter leg of a 30°- 60°- 90° right triangle is 12.5 inches. How long are the longer leg and the hypotenuse?

Answer 1

30-60-90 rule
http://upload.wikimedia.org/wikipedia/commons/4/45/30-60-90_triangle.jpg

Answer 2

A 30-60-90 triangle is very common in math, specifically in trigonometry.
This is one of the things you should memorize.

Answer 3

Start with an equlaterla triangle. All angles measure 60 degrees.

Answer 4

All sides measure 2x.

Answer 5

Now you draw an altitude to the bottom side.
The upper angle of the right triangle on the rigfht side measuses 30 degrees.
The right triangle on the right side is a 30-60-90 triangle.

Answer 6

Now look at the right triangle on the right side.
It has a leg measuring x and a hypotenuse measuring 2x.
We can use the Pythagorean Theorem to find the other leg, h.

Answer 7

Since we are dealing with the length of a segment, we discard the negative solution.
h = sqrt(3) * x
Now you have the ratio of the lengths of a 30-60-90 triangle:
x : sqrt(3) *x : 2x
or simply:
1 : sqrt(3) : 2
This is the result you need to memorize.