Question

A 30-60-90 triangle intersects the unit circle at point (x,y)
, where y=12
. What is the value of x in point (x,y)
? Use the equation of the unit circle to determine the missing coordinate.(1 point)
Responses

1
1

3√2
Start Fraction Start Root 3 End Root over 2 End Fraction

2√2
Start Fraction Start Root 2 End Root over 2 End Fraction

12
Start Fraction 1 over 2 End Fraction

Answer 1

Unit circle: x^2 + y^2 = 1.
With y = 1/2: x^2 = 1 − (1/2)^2 = 1 − 1/4 = 3/4, so x = ±√(3/4) = ±√3/2.
For the 30°/60° triangle in the first quadrant, x = √3/2.