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determine how many solution exist

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2 Answers

    25            15                       15 * sin 84
———— = ———  ---> sin B = —————— 
 sin 84        sin B                           25 

sin B ≈ 0.5967 ---> B ≈ 370 , then measure of angle C = 590
c2 = a2 + b2 - 2ab cos C ---> c2 ≈ 625 + 225 - 750 * 0.5150381 ≈ 463.7
c ≈ 21.5 

sin(B)/15 = sin(84)/25

Solve for B,

B = 36.63 ° <==The only answer for B, since the other solution B = 180 - 36.63 = 143.37 ° is impossible because the sum of angle measures for a triangle must be 180 °.

C = 180 - A - B = 180 - 84 - 36.63 = 59.37 °

c/sin(C) = 25/sin(84)

c = 21.63

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