SOLUTION: the length of the hypotenuse of a 30, 60, 90 triangle is 4. what is the perimeter?

Question 174832: the length of the hypotenuse of a 30, 60, 90 triangle is 4. what is the perimeter?
Answer by actuary(112) (Show Source): You can put this solution on YOUR website!
In a 30-60-90 triangle, the sides of the triangle are in the ratio 1:2:Sqrt[3]
with "2" representing the length of the hypotenuse of the "idealized" triangle. "1" represents the length of the side opposite the smallest angle angle (in this case the 30 degree angle). The length of the other side of the "idealized" triangle is represented by the number Square Root[2].
In your problem, the length of the hypotenuse is 4, so the length of the shortest side is 2 (ratio of 4 to 2 is the same as the ratio 2 to 1). The length of the third side is 3.464 (Use Pythagorean Theorem 4^2 = 2^2 + b^2).
The ratio of the hypotenuse to the third side to the hypotenuse in the "idealized" triangle is 2/Square Root[2] = 1.155.
The ratio of the length of the actual hypotenuse to the actual third side is 4/3.46 = 1.156
I hope that this helps.

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