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

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

Answer 1

To solve this problem, we need to use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since y = 12, we can substitute this value into the equation to solve for x:

x^2 + (12)^2 = 1

x^2 + 144 = 1

Subtracting 144 from both sides:

x^2 = -143

Taking the square root of both sides:

x = ±√(-143)

Since the unit circle is a circle with a radius of 1, x must be a real number. However, the square root of a negative number is not a real number. Therefore, there is no real value for x in this case.