Finding CoordinatesDate: 12/31/96 at 15:57:27 From: Joe Rounceville Subject: Finding the coordinates of the endpoint of a line given its angle from another line Hi, I want to tell you folks thanks a lot for your help. Such speedy responses, too! What a great service you are providing! Anyway, I've got a bit of a mind bender that falls somewhere in the trig arena. I've spent all evening pondering this one, and I've wasted several sheets of scratch paper on it. It doesn't seem like it should be this tough, but I'm still sitting here with no answer, so here goes: Given this: | | B | /\ __________|/__\________ A| \ | \ | \ | C B is at (3,2), A is at the origin, the line BC is 4.123 units long, and angle ABC is 68.616 degrees. How do I determine the coordinates of C? Thanks again for all your help. Joe Rounceville Date: 01/01/97 at 13:54:18 From: Doctor Pete Subject: Re: Finding the coordinates of the endpoint of a line given its angle from another line Hi, The first solution that pops into my head is to use the Law of Cosines to get the distance AC (since we know AB, BC, and angle ABC), then use the Law of Sines to obtain angle BAC. This gives the angle AC makes with the x-axis and hence the polar form of point C. I'll start you off with some of the calculations: (AC)^2 = (AB)^2 + (BC)^2 - 2(AB)(BC)Cos[ABC] = 3^2 + 2^2 + (4.123)^2 - 2*Sqrt[13]*4.213*Cos[68.616] = 19.15857 Sin[BAC] = BC*Sin[ABC]/AC BAC = 61.2959 deg The angle AC makes with the (positive) x-axis is: ArcTan[2/3] - BAC = -27.6058 deg Finally, use the polar-to-rectangular transformation: x = r*Cos[theta] y = r*Sin[theta] to obtain the rectangular coordinates of C. -Doctor Pete, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 01/01/97 at 21:00:46 From: Joe Rounceville Subject: Re: Finding the coordinates of the endpoint of a line given its angle from another line Thanks again for your help, Doctor Pete! Using what you told me I was able to create (for a school project) a realistic animation of someone running. Joe |
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