The Angles of a RoofDate: 11/20/95 at 12:43:5 From: Anonymous Subject: geometry I am trying to build a model house but am having trouble with laying out the roof. The main part of the house has a peaked roof (an "A" frame house); the angle formed when the roof meets the ground is 60 degrees. There is an addition onto the A-frame with a 30 degree angle formed to the walls. /\ / \------+ / \____/_\ / \ | | / \ | | What angle should the addition's roof be cut at so it meets the A-frame roof? Your help would be appreciated. Ben Homan Date: 12/19/95 at 15:14:13 From: Doctor Tarin Subject: Re: geometry Here's an answer. A /\ / E\------+F / \____/_\ / \ | | /________\__|_| B C D Angle ACB and angle ACD are supplements (they add up to 180 degrees). So if angle ACB is 60 degrees, angle ACD is 120 degrees. There is a theorem in geometry that says that AEF and ACD are congruent (they have the same measure), so angle AEF is also 120 degrees. Angle AEF and angle FEC are supplements, so angle FEC must be 60 degrees. Cut that angle, and your roofs should meet. -Doctor Tarin, The Geometry Forum |
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