Answer:
y = 4√6
x = 12√2
Explanation:
See the attached image for a graphical representation of the rule regarding 30-60-90 triangles:
If the triangle's short leg is x, then the long leg is x√3, and the hypotenuse is 2x.
In the given triangle, we can see that the hypotenuse is 8√6, y is the short leg, and x is the long leg.
To solve for x and y, we can work backwards.
y is half the hypotenuse (8√6)
2y = 8√6
y = (8/2) · √6
y = 4√6
x is y times root 3
x = y√3
x = (4√6)(√3)
x = 4 · √18
x = 4 · 3√2
x = 12√2