Question

A 30-60-90 triangle intersects the unit circle at point (x,y)
where y=3√2
. What is the value of x in the point (x,y)
? Use the equation of the unit circle to find the missing coordinate.(1 point)
Responses

3√2

the fraction with numerator square root of 3 and denominator 2

12

1 half

1

1

2√2

the fraction with numerator square root of 2 and denominator 2
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Answer 1

There’s a mistake: y = 3√2 (> 1) cannot lie on the unit circle (x² + y² = 1) because y² would already be 18. If you meant y = √3/2 (common for a 30–60–90 on the unit circle), then

x² = 1 − y² = 1 − (√3/2)² = 1 − 3/4 = 1/4, so x = ±1/2.

For the usual 30–60–90 in the first quadrant, x = 1/2. (If y were truly 3√2, x would be imaginary.)