Given a triangle where angle A is equal to 2B and angle C is obtuse, which angles give theminimum perimetre?
2007-05-14 17:01:42 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Can you fill in some computational details? That's whats giving me a hard time.
2007-05-14 17:47:22 · update #1
You want to minimize a+b+c, the perimeter, where each side is opposite to the angle A, B, and C respectively. However, a, b and c will depend on the angles, so you have to come up with a relation based on dependence with one and only one angle. I'd pick B, since it is smallest. The law of sines and the double angle will give us "a" and "b". The law of cosines will give us c in terms of a and b. Since the angle C is obtuse, this fixes the sign of the cross term 2abCosC. Then you can put it all together, take the derivitive, and find the minimum.
2007-05-14 17:16:15 · answer #1 · answered by cattbarf 7 · 0⤊ 0⤋
angle B is opposite the shortest length line
as it is the smallest angle
but if the angles are fixed how can the perimeter change
2007-05-14 17:19:52 · answer #2 · answered by Maths Rocks 4 · 0⤊ 0⤋