Explanation:
you skipped a few things in your problem description.
particularly the name of the angle.
so, I call the angle x.
if I understand you correctly, we need to find
cos(x)
remember the trigonometric triangles inside their circle.
any legs of the triangles going up/down are sine of the angle at the center of the circle.
and the legs going left/right are cosine.
the baseline of all these triangles are the radius of the circle.
since in the standard definition the radius of the circle is 1, we have to multiply sine and cosine by the actual radius for any larger or smaller triangles/circles involved.
quadrant II means the upper left quadrant (negative x, positive y).
so, based on all this, we know point c is on the upper left arc quarter of the circle.
is y coordinate is 8, so, the up/down leg of the imaginary triangle inscribed into this circle goes up by 8 units.
so,
sin(x) × radius = 8
sin(x) × 10 = 8
sin(x) = 8/10 = 0.8
now we have multiple ways to get the length of the left/right leg and then therefore cos(x).
there is e.g. Pythagoras
(cos(x)×10)² + 8² = 10²
100×cos²(x) + 64 = 100
100×cos²(x) = 36
cos²(x) = 36/100
cos(x) = 6/10 = 0.6
or we could calculate x out of sin(x) and then calculate cos(x) :
sin(x) = 0.8
x = 53.13010235...°
cos(x) = 0.6
or a few other possibilities. but I don't want to confuse you.