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

Question

Right triangle y, x, 6

X=? Y=?

Answer x= 3sqrt3 y= 3

Answer 1

In a 30-60-90 triangle, the sides opposite the angles measure x, 2x, and x√3 (where x is the shortest side).

Here, we know that the shortest side (opposite the 30 degree angle) is y, which means:

y = x

The side opposite the 60 degree angle is x√3, which means:

x√3 = 6

Solving for x:

x = 2√3

And solving for y:

y = x

y = 2√3

simplifying:

x = 2√3 = 3√3/2

y = 2√3 = 3√3/2

So, in simplest radical form, x = 3√3/2 and y = 3√3/2 (or we can express both as 3√3).