Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is smaller than ∠B2.)

Question

a = 34, c = 43, ∠A = 39°

∠B1 =


°
∠B2 =


°
∠C1 =


°
∠C2 =


°
b1 =


b2 =

Answer 1

sinC/c = sinA/a
sinC/43 = sin39°/34 = 0.01851
sinC = .7959
so, C = 52.74° or 127.26°
Since A+B+C=180, B=88.26° or 13.74°

Now use those two values for B to get B, using

b/sinB = 1/0.01851 = 54.0265

Answer 2

Thank you so much! I am just trying to figure out how to solve for b1. I am confused as to how you got the 1 and why you used 0.01851 when you said to use the two values for B to get B (the two values are 88.26 and 13.74)

Answer 3

I mean, that for each value of c, there is a corresponding value of b.

Since B can be either 88.26 or 13.74,

b1/sin(88.26) = 54.0265, so b1=54.10
or
b2/sin(13.74) = 54.0265, so b2=12.86