Question

Find all solutions to the following triangle. (Round your answers to one decimal place. If either triangle is not possible, enter NONE in each corresponding answer blank.)
A = 115.2¡ã, a = 43.6 cm, b = 23.1 cm
First triangle (assume B ¡Ü 90¡ã):




B

=

¡ã



C

=

¡ã



c

=

cm



Second triangle (assume B' > 90¡ã):




B'

=

¡ã



C'

=

¡ã



c'

=

cm

Answer 1

I am not familiar with your symbols.

sinB/b = sinA/a.
sinB/23.1 = sin115.2/43.6
Multiply both sides by 23.1
sinB = 23.1*sin115.2/43.6 = 0.47939
B = 28.6o.

CosA = b^2+c^2-a^2/2bc.
Cos115.2 = (23.1)^2+c^2-(43.6)^2/46.2c
-0.42578 = (533.61+c^2-1901)/46.2
-0.42578 = (-1367.39+c^2)/46.2c
-0.42578c = (-1367.39+c^2)/46.2
-19.67c = -1367.39+c^2
-c^2-19.67c = -1367.39
c^2+19.67c-1367.39 = 0.
c = 28.43 cm.

C = 180-115.2 -28.6 = 36.2o