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

12
Start Fraction 1 over 2 End Fraction

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

1
1

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

Answer 1

To find the value of \( x \) given that \( y = 12 \) in the context of a unit circle, we start with the equation of the unit circle:

\[
x^2 + y^2 = 1
\]

Given \( y = 12 \), we substitute this value into the equation:

\[
x^2 + 12^2 = 1
\]

Calculating \( 12^2 \):

\[
x^2 + 144 = 1
\]

Next, we isolate \( x^2 \):

\[
x^2 = 1 - 144
\]
\[
x^2 = -143
\]

Since \( x^2 \) cannot be negative, there is no real value of \( x \) that meets the condition of a point on the unit circle with \( y = 12 \). Therefore, the point (x, y) with \( y = 12 \) is not on the unit circle.

Thus, no values from the options provided are correct as they all assume \( y \) would be a real valid coordinate on the unit circle, which it is not in this case.

The conclusion is that there is no real value of \( x \) corresponding to \( y = 12 \) on the unit circle.