A building’s roof has “6 in 12” slope in the front and back and “8 in 12” slope on the sid...

A building’s roof has “6 in 12” slope in the front and back and “8 in 12” slope on the sides. Determine the angles  α and β that should be used for cutting sheets of plywood so they properly meet along edge A B of the roof. Hint: Write the position vector  (where B is some point along the edge-of the roof) two ways:  and  Then use the roof slopes to help write  and  such that the magnitudes of the two expressions for  are the same.

Figure P2.89