Find the length of x and y in the 30-60-90" triangle. Leave answer in simplest radical form

Question

Right triangle y, x, and 6

X=? Y=?

Answer x= 3sqrt3 y= 3

Answer 1

In a 30-60-90 triangle, the sides are in a ratio of x : x√3 : 2x.

Here, we know that one of the sides is 6, which corresponds to the longest side, 2x. Thus, we have:

2x = 6
x = 3

So, the other side adjacent to the 30 degree angle, which is x√3, is:

x√3 = 3√3

And the remaining side opposite to the 60 degree angle, which is x/2, is:

x/2 = 3/2

Therefore, the length of x is 3√3 and the length of y is 3.