Why does a/SinA = b/SinB = c/SinC?Date: 08/12/97 at 07:57:39 From: Glen Gibson Subject: Trigonometry I was just playing aroung with a proof of a triangle and came across the fact that a/SinA = b/SinB = c/SinC. Why? Date: 08/12/97 at 08:47:05 From: Doctor Jerry Subject: Re: Trigonometry Hi Glen, Draw a triangle ABC, with AC horizontal and B above AC, maybe somewhat to the left of the center point of AC. This is so that we can be looking at the same triangle, more or less. Draw a line from B perpendicular to and intersecting the line AC at E. Let BE = h. Let a be the side opposite angle A, b opp. B, and c opp. C. Note that sin(A) = h/c and sin(B) = h/a. Solve each equation for h and equate to get c*sin(A) = a*sin(C). This is part of the law of sines. You can finish by drawing another altitude. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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