Question 928226
{{{drawing(400,200,-2,42,-10,12,
green(triangle(0,0,40,0,40,10.72)),
line(-2,0,42,0),line(30,8.04,33.86,9.07),
line(30,8.04,29.48,9.97),line(33.86,9.07,33.34,11),
line(33.34,11,29.48,9.97),red(arc(0,0,10,10,-15,0)),
locate(6,2.6,red(15^o)),locate(3,-.1,horizontal),
green(triangle(31.67,9.52,31.67,-5.48,35.42,-4.48)),
green(triangle(31.67,9.52,31.67,-5.48,27.95,8.55)),
arrow(31.67,9.52,31.67,-5.48),arrow(31.67,9.52,35.42,-4.48),
arrow(31.67,9.52,27.95,8.55),locate(32,-.1,90),
locate(33.5,6,90*cos(15^o)),red(arc(31.67,9.52,10,10,75,90)),
red(arc(31.67,-5.48,10,10,255,270))
)}}} The weight (90 lb force), and its components are represented by arrows.
The angles between the weight and the component perpendicular to the inclined plane is the same {{{15^o}}} angle as between the horizontal and the inclined plane (just rotated {{{90^o}}} and shifted).
The components of the weight are represented by the arrows along the legs of those green right triangles that have the weight arrow as the hypotenuse,
and a {{{15^o}}} angle marked by a red arc.
The perpendicular component's magnitude is
{{{"(90"}}}{{{"lb)"}}}{{{cos(15^o)=86.9}}}{{{lb}}}
The parallel component's magnitude is
{{{"(90"}}}{{{"lb)"}}}{{{sin(15^o)=23.3}}}{{{lb}}}