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 2√2 Start Fraction Start Root 2 End Root over 2 End Fraction 1 1 12 Start Fraction 1 over 2 End Fraction 3√2

1 answer

The equation of the unit circle is given by:

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

In this case, we know \( y = 12 \). We can substitute \( y \) into the equation:

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

Calculating \( 12^2 \):

\[ x^2 + 144 = 1 \]

Now, we can isolate \( x^2 \):

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

Since \( x^2 \) cannot be negative, this indicates that there are no real values of \( x \) corresponding to the point on the unit circle with \( y = 12 \). Therefore, the point \( (x, 12) \) does not intersect the unit circle.

The value of \( x \) cannot be determined as part of a point on the unit circle.