I have a triangle, which I drew out and uploaded here: http://www.eggloaf.com/math.PNG (not drawn to scale, of course). I am trying to find the maximum value side Y can be while keeping the given's the same (that angle X is 6.08 degrees and side X is 1). Can anyone explain to me how I would solve this? I think optimization would be the way to go, but I'm not sure where to go from where I am. So far I have found that Side Y=(SinY/.1059) through the law of sines. Any ideas?
2007-02-03 05:14:59 · 4 answers · asked by Beeflog 1 in Science & Mathematics ➔ Mathematics
By law of sines,
y/sin Y = x/sinX
y
= sinY/sin60.8
y(MAX)
= 1/sin60.8
= 1.1456
Reason:
maximum sinY = 1
2007-02-03 05:34:59 · answer #1 · answered by sahsjing 7 · 0⤊ 0⤋
The easiest way to understand this geometrically is to extend lines Y and Z to infinity. Then get a circle of radius 1, center it on line Y, and move it until line Z just touches it. That gets you the maximum value for Y. It also means that angle Y is 90°, which makes the problem so much easier. We have:
Sin (6.08°) = X / Y = 1 / Y, or
Y = 1 / Sin (6.08°) = 9.44
By the way, the PICTURE asks for the max value of side Z, but the solution is exactly the same. Slide the circle on line Z instead.
2007-02-03 14:12:17 · answer #2 · answered by Scythian1950 7 · 0⤊ 0⤋
Well value for angle Y is on (0,180-6.08) not inclusive. Take the extreme case angle X = 6.08, angle Y = 173.92. Then just solve for length of side Y.
2007-02-03 13:29:01 · answer #3 · answered by x 4 · 0⤊ 0⤋
I believe that the right triangle has the maximum length in the long side. Then length is about 9.44 with an angle of 83.2 degrees opposite.
2007-02-03 14:24:46 · answer #4 · answered by anonimous 6 · 0⤊ 0⤋