Constructing a PyramidDate: 05/28/99 at 10:09:24 From: daniel Subject: Constructing angles for a pyramid I am trying to build a 6 ft. pyramid out of copper. I have an 8 ft. base but I am having trouble getting the right angle, 51 deg 51 sec, for the height I want. I tried cutting the four 8 ft. sections to exactly 6 ft. but that doesn't work. Date: 05/28/99 at 16:58:45 From: Doctor Peterson Subject: Re: Constructing angles for a pyramid Hi, Daniel. Sounds like a big project! I'm not sure what your 51 degree angle is, but here's how I understand the dimensions you gave: base 8 x 8 feet, height 6 feet. * /|\ / | \\ / || \ \ / || \ \ / | | \ \ / | |6 \ + / | | / \ \ / |/ | \ \ / / | | \ \ / / | | \ \ + | | \ \ \ | | \\ \ | + \\ \ | \ \ \ | \ \ \ | \ + 8 \ | \ / \ | \ / \ | + \ | / 8 \| / + We can figure out the dimensions of each of the four side panels (faces) by a series of right triangles. First we look at the triangle formed by the altitude of the triangle (6), the perpendicular from the foot of the altitude to one side of the base (4), and the slanted altitude of the face (a): * /|\ / | \\ / ||| \ \ / ||| \ \ / | || \ \ / | | | \ + / | 6| | / \ \ / |/ | | \ \ / / | | | \ \ / / | | |a \ \ + | | | \ \ \ | | | \\ \ | + | \\ \ | \ | \ \ | \ | \ \ | 4\ | + 8 \ | \| / \ | \| / \ | + \ | / 8 \| / + Using the Pythagorean Theorem, a^2 = 6^2 + 4^2 = 36 + 16 = 52 so a = sqrt(52) = 7.2111 feet. Now we can use the right triangle formed by half of this face: + /|\ / | \ / | \ / | \ / | \ / | \ / | \ s/ | \s / | \ / | \ / |a \ / | \ / | \ / | \ / | \ /A 4 | 4 A\ +----------------+----------------+ We can find the length of the sides of this triangle (s) by the Pythagorean Theorem again: s^2 = 4^2 + a^2 = 16 + 52 = 68 so s = sqrt(68) = 8.25 feet. If you want the angle A, we can find that using trigonometry: A = arctan(a/4) = arctan(1.8) = 60.98 degrees Since I don't see any 51 degree angles, I may be misinterpreting what you want to do, but this should at least give you some ideas for how to do it. If you need more help, let me know where I'm wrong so I can try again. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 06/12/99 at 07:14:50 From: daniel f gordon jr Subject: Re: Constructing angles for a pyramid Thank you very much. It helped a lot. |
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