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determine how many solution exist

< = angles

determine how many solution exist

<A = 84 , a = 25 , b=15
Solutions ----
< B = __ <C = ___ c=__
<B= __ <C=__ c=__

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Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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    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 

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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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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