Question

In right triangle XYZ, ∠Y is the right angle and m∠X = 60°. If YZ = 4, what is XY?

Answer 1

We can use the trigonometric ratios of a 30-60-90 triangle to find the length of XY. In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

Since ∠X is 60°, we know that ∠Z is 30°, and we can set up the following equation:

XY / 4 = 2 / √3

To solve for XY, we can multiply both sides of the equation by 4√3:

XY = 4 * 2 / √3

Simplifying the right side, we get:

XY = 8 / √3

To rationalize the denominator, we can multiply the numerator and denominator by √3:

XY = (8 / √3) * (√3 / √3)

Simplifying, we get:

XY = 8√3 / 3

Therefore, the length of XY is 8√3 / 3, which is approximately 4.62 units.