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

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 AB 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 such that the magnitudes of the two expressions for are the same.