Question

Find the value of X and the value of Y

Answer 1

This is a 30-60-90 triangle. In a 30-60-90 triangle, the longer leg is √3 times longer than the shorter leg, and the hypotenuse is twice the length of the shorter leg.

Longer leg: shorter leg * √3

Hypotenuse: shorter leg * 2

In the diagram, the shorter leg would be 18/2 = 9. x is the longer leg, so x would be 9√3. y is the hypotenuse, so y would be 9*2 = 18.

x (longer leg) = 9 * √3

y (hypotenuse) = 9 * 2 = 18

$\boxed {D)~x= 9 \sqrt 3,~ y = 18}$