Solving Oblique Triangles

Problem : In Triangle ABC, a = 4 , b = 3 , and B = 122 ^o . Is a triangle determined? If so, how many?

Problem : If the side opposite the given angle is longer than the other given side, how many triangles are determined?

Problem : Solve Triangle ABC given that a = 12 , b = 7 , and B = 36 ^o .

Solution for Problem 3 >>

sin(A) = 1.07 . No solution. Sine never exceeds one.

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Problem : Solve Triangle ABC given that a = 7 , b = 6 , and B = 45 ^o .

Solution for Problem 4 >>

sin(A) = .82 . A 55.6 ^o or 124.4 ^o . This is an example of case three discussed in the text. The first possible triangle, an acute triangle, has parts a = 7 , b = 6 , c 8.3 , A 55.6 ^o , B = 45 ^o , C 79.4 ^o . The second possible triangle, and obtuse triangle, has parts a = 7 , b = 6 , c 1.6 , A 124.4 ^o , B = 45 ^o , and C 10.6 ^o .

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Problem : Two sides of a triangle and an angle opposite one of them is given. There is no solution to the triangle. What must be true of the side opposite the given angle and the other given side?