a 30-60-90 triangle intersects the unit circle at point (x,y), where y = 1/2. what is the value of x in point (x,y)? use the equation of the unit circle to determine the missing coordinate
In a unit circle, the equation is typically given as x² + y² = 1, where (x, y) represents a point on the circle. Since we already know that y = 1/2, we can substitute this value into the equation:
x² + (1/2)² = 1
x² + 1/4 = 1
To solve for x², we can subtract 1/4 from both sides of the equation:
x² = 1 - 1/4
x² = 3/4
Taking the square root of both sides, we get:
x = ± √(3/4)
Since we are dealing with a 30-60-90 triangle, x should be positive because the x-value represents the horizontal distance from the origin. Therefore, we have:
x = √(3/4)
Simplifying the square root, we have:
x = √(3)/√(4)
x = √(3)/2
Hence, the value of x in the point (x, y) where y = 1/2 is x = √(3)/2.