determine how many solution exist

Question

< = angles

determine how many solution exist

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

Answer 1

    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 

Answer 2

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