CH 2200 Lecture 20: Chinese common words 37

A group of architects is designing a house to be built in your city. A line drawing of the house is shown below. The back of the house faces due south, and is largely windows. At 12 noon local time (this is not the same as 12 noon standard time, but is close to standard time) the sun is as high in the sky as it will be that day. On the Vernal equinox and autumnal equinox (look up these terms) the sun's highest point is 90 minus the latitude in degrees. (Why?) At the summer solstice, the sun (at local noon) is about 23 degrees above the position at the equinoxes, and at the winter solstice, the sun at its highest is about 23 degrees lower than it is at the equinoxes. · Since you want the winter sun (to warm up the room) and you don't want the summer sun, the house is designed to let in (most of) the winter sun, and little of the summer sun. The picture shows the sun at the Vernal equinox or autumnal equinox. The roof is pitched so that, when viewed from floor level inside the house and 10 feet in from the back wall of the house, the sun is right at the end of the overhang. In addition, the line to the sun from a point on the floor (inside the house) that is 10 feet back from the outside wall is perpendicular to the roof overhang (as shown in the line drawing). Examine the triangle whose vertices are the point 10 feet back on the floor, the point where the line to the sun intersects the back wall, and the top of the back wall.) The house is 27 feet from front to back (north to south). Find as many angles as you can. Only then use Trigonometry to find the missing distances. Find all the dimensions of the house that are not already given in the above figure at your latitude (Atlanta) at the Vernal equinox or autumnal equinox. Keeping the house the same, find all the dimensions of the house that are not already given in the above figure at your latitude (Atlanta) at the summer and winter solstices. What is the pitch of the roof? How long is the overhang?