Hi
The grey circle is a pivot, and the ground is rough.
Why are the vertical and horizontal components of the reaction "R", Rcos(a) and Rsin(a) respectively?
Thankyou
A little basic geometry:
The horizontal line at the bottom of the diagram is parallel to the horizontal line coming from where R meets the inclined plane (the Rx component). Thus the angle between the Rx component and the inclined plain is the same as the angle between the inclined plain and the horizontal, a. (Alternate interior angles are equal.)
Since R makes a right angle with the inclined plain, the angle between R and Rx is 90 - a. Again, since Rx and Ry are perpendicular the angle between R and Ry is a. Now find your components. The angle a is on the adjacent side to the Ry component, so $\displaystyle R_y = R~cos(a)$. etc.
-Dan