solve for the value of x and y. Leave your answer in simplest radical form.
30-60-30 right triangle
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In a 30-60-90 right triangle, the sides are in the ratio of 1:√3:2. Therefore, if we let the shorter leg be x, then the longer leg is x√3 and the hypotenuse is 2x.
From the Pythagorean theorem, we have:
x^2 + (x√3)^2 = (2x)^2
x^2 + 3x^2 = 4x^2
4x^2 = 4x^2
So, x can be any non-zero value, but to simplify, let's say x = 1. Then, the lengths of the sides are:
shorter leg (x) = 1
longer leg (x√3) = √3
hypotenuse (2x) = 2
Therefore, the values of x and y in this 30-60-30 right triangle are x=1 and y=√3.