In triangle ABC b = 0.3, angle A = 32 degrees, angle B = 70 degrees. Find the unknown elements of the triangle.

given
triangle ABC
side b = 0, 3
angle A = 32 degrees
angle B = 70 degrees
find a side with
and angle C
decision
since the sum of the angles of the triangle is 180 degrees, then we find the angle C
in order to find the angle C, you need to subtract the sum of two known angles from 180 degrees
the sum of two known angles equals angle A + angle B = 32 degrees + 70 degrees = 30 degrees + 2 degrees + 70 degrees = 100 degrees + 2 degrees = 102 degrees
angle C = 180 degrees – 102 degrees = 100 + 80 – 100 – 2 = 80 + 2 = 78 degrees
then we will find the side with, since
a = b * tg A = 0. 3 * tg 32, then
c = b / sin B = 0. 3 / sin 70
answer: angle С = 78 degrees
c = 0. 3 / sin 70