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

hypotenuse: 6
angle: 60°

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1 answer

In a 30°-60°-90° triangle, the opposite side of the 60° angle is √3 times smaller than the hypotenuse and the adjacent side of the 60° angle is half the length of the hypotenuse.

Using this, we can say that:

y = opposite side of the 60° angle = (√3/2) * 6 = 3√3 units
x = adjacent side of the 60° angle = 6/2 = 3 units

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