Building a Manger
Date: 12/03/2001 at 22:39:44 From: Anne Markle Subject: Angles for a building I am building a manger with a base of 11" (A), one wall 7 1/2" high (B) and the other wall 6" high (C). Both walls meet the base at 90-degree angles. My question is: What would the length of my roof be and what would be the two angles of the walls meeting the roof? Thanks.
Date: 12/04/2001 at 01:08:51 From: Doctor Jeremiah Subject: Re: Angles for a building Hi Anne, Many people write to us asking how math fits into the real world. I see that isn't your problem, though! + | + | + | + | + | | 7 1/2 6 | | | | +--------11---------+ This is a side view of your building. The roof must go on top, but first you need to know how long it will be. Lets redraw this as a rectangle and a triangle: + | + 1 1/2 + | + +--------11---------+ | | 6 6 | | | | +--------11---------+ You will notice that the angle where the 11" top of the rectangle meets the 1 1/2" extension is 90 degrees. Have you heard of Pythagoras? He is famous for his method of calculating the third side of a triangle that has a 90 degree angle, the Pythagorean theorem. Pythagoras said that the square of the length of the long side was equal to the sum of the squares of the other sides. So if we call the length of the roof "R" then because of Pythagoras we can say: R squared = 1.5 squared + 11 squared R squared = 1.5 times 1.5 + 11 times 11 R squared = 2.25 + 121 R squared = 123.25 And if R squared is 123.25 then R is the square root of 123.25, which is 11.1 inches. But wait! Roofs usually hang over the edge, so you are going to want to make it longer than that anyway. I would suggest 12 inches so that you get a decent size for the eaves. As for the angles, they require some trigonometry to calculate. It turns out that we don't need to know the length of the third side to calculate the angles. a + | + 1 1/2 + | + +--------11---------+ b I have labeled the two angles a and b. The angle at a can be calculated by taking the tangent of 11/1.5, and the angle at b can be calculated by taking the tangent of 1.5/11 - but you will need a calculator to do that. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/
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