Solve for x and y in a 30-60-90 right triangle with hypotenuse 6

Question

Solve for x and y in a right triangle with one angle 60°, hypotenuse length 6, right angle at the vertex between x and y.

Accepted Answer

x=3, y=3√3

Answer

Step 1: Identify the triangle is a 30-60-90 special right triangle. In this triangle, the side opposite 30° is half the hypotenuse, the side opposite 60° is hypotenuse × √3/2. Step 2: The side x is opposite the 30° angle, so x = 6/2 = 3. Step 3: The side y is opposite the 60° angle, so y = 6 × √3/2 = 3√3.