Solve ΔABC. (Round your answers to three decimal places. If there is no solution, enter NO SOLUTION.)

Question

β = 145.206°,     b = 0.851,    c = 0.483

α	=
γ	=	°
a	=

Answer 1

The terminology is a little confusing, but I'm guessing the picture looks like this:

We need to be careful because this is set up as a POSSIBLE ambiguous case (SSA). but, in looking a little deeper, the side opposite the angle given is the longest side so we are OK. We can use the law of sines.

So:

sin(β)/b = sin(γ)/c

sin(145.206°)/0.851 = sin(γ)/0.483

0.483sin(145.206°)/0.851 = sin(γ)

sin(γ) = 0.3238697

γ = sin^-1(0.3238697) = 18.897°

α = 180 - 145.206 - 18.897 = 15,897°

sin(α)/a = sin(β)/b

sin(15,897)/a = sin(145.206°)/0.851

a = 0.851sin(15,897)/sin(145.206°)

a = 0.408