Examples of 306090 Triangles
EXAMPLE 1:  Find the exact length of the side marked x in the triangle on the right: 
SOLUTION: "Exact" means we must give a simplified answer involving square roots. In this triangle, side is the hypotenuse, so we set its length to 2a: 8 = 2a. Thus, a = 4, and since side is adjacent the 30^{o} angle, its length is , so in this case .
EXAMPLE 2:  Find the exact length of the hypotenuse in this right triangle: 
SOLUTION:

Comparing with a standard 306090 triangle, the given side is , so , and . We need to simplify this by rationalizing the denominator. We do that by multiplying top and bottom by : . The hypotenuse is . 
