I had planned to go over to the college today to take the last of the regular Exams. But as I was working on the practice problems, it turns out I'd missed a section in one chapter. Specifically, Heron's Area Formula
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Hmm...If you are given an acute angle and 2 sides, if the angle is between the sides (Side-Angle-Side), there's only one possible triangle. If you're given Angle-Side-Side, there may be one or two possible triangles, so I assume that's the problem you're talking about.
That means you know Angle a, Side A, and Side B. Use the law of sines to find Angle b: sin(a)/A=sin(b)/B ==> b1 = Arcsin(B/A * sin(a)). Keep in mind that the Arcsin gives you the smallest of an infinite number of solutions. so b2=180-b1 may also be a valid solution. (All the other solutions would give you an angle greater than 180, which is impossible for a triangle.)
(Lastly, Angle c = 180-a-b, and then use the law of sines to find Side C.)
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That means you know Angle a, Side A, and Side B. Use the law of sines to find Angle b: sin(a)/A=sin(b)/B ==> b1 = Arcsin(B/A * sin(a)). Keep in mind that the Arcsin gives you the smallest of an infinite number of solutions. so b2=180-b1 may also be a valid solution. (All the other solutions would give you an angle greater than 180, which is impossible for a triangle.)
(Lastly, Angle c = 180-a-b, and then use the law of sines to find Side C.)
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But good luck on the test! I'm betting you get another A.
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