Question

A 30-60-90 triangle intersects the unit circle at point (x,y), where y = 1/2. What is the value of x in point (x,y)? Use the equation of the unit circle to determine the missing coordinate.

1/2

√3/2

√2/2

1

Answer 1

Use x^2 + y^2 = 1. With y = 1/2:

x^2 + (1/2)^2 = 1 → x^2 + 1/4 = 1 → x^2 = 3/4 → x = ±√(3/4) = ±√3/2.

For the 30° point on the unit circle (0 ≤ angle ≤ 90°) x is positive, so x = √3/2.