A special right triangle drawn in Quadrant 1 intersects the unit circle at point (x, y) where y = 2√2
. What is the x-coordinate? (1 point)
Responses
2√2
the fraction with numerator square root of 2 and denominator 2
3√2
the fraction with numerator square root of 3 and denominator 2
1
1
45 degrees
The x-coordinate can be found using the Pythagorean theorem. Since the y-coordinate is 2√2, we can calculate the length of the hypotenuse using the formula a^2 + b^2 = c^2, where a and b represent the legs of the triangle and c represents the hypotenuse.
In this case, the length of the hypotenuse is √(a^2 + (2√2)^2) = √(a^2 + 8).
Since the triangle intersects the unit circle, the length of the hypotenuse is equal to 1. Therefore, we can write the equation √(a^2 + 8) = 1.
Solving this equation gives a = √(-7), which is not a real number. Therefore, there is no x-coordinate that satisfies the given conditions.