how to find lenght of indicated side in 30-60 rt triangle

[king&i]

how do you find the lenght of an indicated side in a 30-60 right triangle?If they only have one side of the triangle`s degree, either 30 or60 degree and a lenght on one side? example: one leg=9 and it is has a 30 degree angle what will be the lenght of the other leg? or if they have the lenght of the hypotenuse?

[stapel_eliz]

Draw an equilateral triangle. Draw the altitude line from the vertex at the peak down to the midpoint of the base, splitting the triangle into two right triangles.

Since an equilateral triangle is a 60-60-60 triangle, then a right triangle formed from half of an equilateral triangle has to be a 30-60-90 triangle. (Study your picture until you're sure about this!)

Let the sides of the original triangle have a length of 2. Then half of a side is 1. Use the Pythagorean Theorem to find the length of the altitude line.

Since any 30-60-90 triangle will be "similar", in the geometrical sense, to the one you've just drawn. That is to say, the hypotenuse will always be twice the length of the shorter leg, and the longer leg will always be times as long as the shorter leg.