Answer: A) 126.6
Step-by-step explanation:
Since we know ∠B = 85° and ∠C = 53°, we can use the Triangle Sum Theorem (angles of a triangle = 180°) to calculate ∠A.
∠A + ∠B + ∠C = 180
∠A + 85 + 53 = 180
∠A + 138 = 180
∠A = 42
Now we have:
A = 42 B = 85 C = 53
a = 85 b = ??? c = ???
We have all of the information for ∠A and side a so we can use the Law of Sines to find b (AC).
[tex]\dfrac{\sin 42}{85}=\dfrac{\sin 85}{b}\\\\\\b(\sin 42)=85(\sin 85)\\\\\\b=\dfrac{85\sin 85}{\sin 42}\\\\\\b=\large\boxed{126.547}[/tex]
