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
A 30-60-90 triangle is a special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. If this triangle intersects the unit circle at a point (x, y) where y = 1/2, it means that we're looking at the point corresponding to the 60-degree angle, because the y-coordinate for that point in the unit circle is always positive and less than the x-coordinate (which corresponds to the 30-degree angle in this context).
In a unit circle, the equation is x^2 + y^2 = 1. We already know that y = 1/2. We can plug that into the equation to find the value of x:
x^2 + (1/2)^2 = 1
x^2 + 1/4 = 1
x^2 = 1 - 1/4
x^2 = 3/4
x = sqrt(3/4)
x = sqrt(3)/2
So, the x-coordinate of the point where the 30-60-90 triangle intersects the unit circle, and y-coordinate is 1/2, is x = sqrt(3)/2.