9. In triangleABC, A=31degrees, AC=32cm, and CB=20cm. Find all possible values of B.

Question

B=34.5
B=55.5
B=59
B=93.5
B=124.4

10. In triangleABC, AB=8, BC=9, and CA=11. Find the measure of the smallest angle.
80.4
53.8
52.3
45.8

Thank you! I really need help on these

Answer 1

law of sines
(sin 31 ) / 20 = (sin B ) / 32
sin B = (32/20) sin 31
= 0.824
so
B = 55.5 degrees
but watch out, same sin in quadrant 2
180 - 55.5 = 124.5 degrees

Answer 2

going by the law of sines it is likely to be the angles opposite the shortest side, ,C
law of cosines
c^2 = a^2 + b^2 - 2 a b cos C
your turn :)

Answer 3

9. B) m∠B = 55.5°; E) m∠B = 124.5°
10. D) 45.8°