During the hottest months in Austin, the angle which the nonday sun (shining from the south) makes with the horizontal varies from 70 to 80 degrees. During the coldest months, this angle ranges from 36 to 39 degrees. A house has a south facing window 6 feet in height which starts 5 feet above the ground. There is a horizontal overhang 2 feet above the top of the window.
a.) How long (i.e. how far sticking out) must the overhang be in order to shade the window completely at noontime during the hottest months?
b.) What is the longest the overhang could be to avoid shading any part of the window during the coldest months?
c.) How could you design an overhang to achieve both the goal in a. and the goal in b. (You may alter the horizontal assumption and the assumption of being 2 feet above the window.)