Question

How to determine the acute angle between the line 2x+3y=6 and the y axis?

Answer 1

$2x+3y=6\\3y=-2x+6\ \ \ /:3\\y=-\frac{2}{3}x+2\\\\the\ angle\ between\ the\ line\ and\ the\ x\ axis-\alpha\\\\tg\alpha=-\frac{2}{3}\approx-0.666...\to\alpha\approx124^o\\\\the\ acute\ angle\ between\ the\ line\ and\ the\ y\ axis\ is\ 124^o-90^o=34^o$