Geometry

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2 total messages Started by benjohnson Thu, 20 Aug 1998 00:00

#18

Author: benjohnson
Date: Thu, 20 Aug 1998 00:00

3 lines
685 bytes

Could someone tell me the procedure to make a triangle knowing its
perimeter and the
amplitudes of its tree angles .

Re: Geometry

#19

Author: Rob Morewood
Date: Sat, 22 Aug 1998 00:00

31 lines
1647 bytes

benjohnson (benoitcarlier@hotmail.com) wrote:
: Could someone tell me the procedure to make a triangle knowing its
: perimeter and the amplitudes of its three angles.

Let the unknown sides be 'a', 'b', and 'c'.
Represent the (known) opposite angles by capitals:  'A', 'B', and 'C'.
We also know the perimenter:  P=a+b+c.

The SINE LAW relates angles to sides:

      a          b          c
    ------  =  ------  =  ------
    Sin(A)     Sin(B)     Sin(C)

I'll leave the algebra to you.
Solve the Sine Law for 'a' and 'b' in terms of 'c'.
Substitute for 'a' and 'b' in the equation for P and solve for 'c':

c = P*Sin(C)/[Sin(A)+Sin(B)+Sin(C)].

Now, knowing one side along with the angles, it should be easy to
draw the triangle.
 _
|/|\/|                          ||   Maths & Computer Science
|\|  |orewood@south.sd41.bc.ca  ||  Beautiful British Columbia
                                            (Canada)

P.S.  If you are looking for a strictly Euclidean construction
(straight edge and compass), it can be done.  Addition, multiplication,
division, and the Sin function can all be done with straight edge
and compass, but I'm too lazy to do the conversion and optimization.

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