The positive x-axis passes through the 1st and 4th quadrants.
The line y = 3x increases from left to right because the slope is positive, so it passes through the 1st and 3rd quadrants.
Therefore, theta drawn in standard position will be an acute angle in the first quadrant.
We now find a point in the first quadrant on which the line y = 3x passes through. The simplest point with integral coordinates is (1, 3).
If we were to draw a triangle, the side opposite theta would have measure 3 and the side adjacent theta would have measure 1. By Pythagorean Theorem:
(3)^2 + (1)^2 = h^2
10 = h^2
h = +-sqrt(10)
But since we're talking about the hypotenuse, h>0. Therefore, sintheta = "opposite"/"hypotenuse" = 3/sqrt(10) = (3sqrt(10))/10.
Hopefully this helps!
