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 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

Answer 1

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.