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)

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

GPT-4o mini · Answer

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.