Question

Someone pls help im so close

Answer 1

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).

$\dfrac{\sin 42}{85}=\dfrac{\sin 85}{b}\\\\\\b(\sin 42)=85(\sin 85)\\\\\\b=\dfrac{85\sin 85}{\sin 42}\\\\\\b=\large\boxed{126.547}$