Question

find the value of x and y.

Explanation:

Step1: Find x (opposite 30°)

In a 30-60-90 triangle, the side opposite 30° is half the hypotenuse. Hypotenuse = 6, so \( x = \frac{6}{2} = 3 \).

Step2: Find y (adjacent to 30°)

Use Pythagorean theorem or 30-60-90 ratios. For 30-60-90, the longer leg (y) is \( \text{shorter leg} \times \sqrt{3} \). So \( y = 3\sqrt{3} \), or via \( y = \sqrt{6^2 - 3^2} = \sqrt{27} = 3\sqrt{3} \).

Answer:

\( x = 3 \), \( y = 3\sqrt{3} \)