Answer:
AC ≈ 126.6
Step-by-step explanation:
The law of sines can be used to find the side length of interest in this triangle. It tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
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missing angle
In order to use the law of sines, we must have a side length and its opposite angle. Here, the angle opposite the given side is unmarked, so we need to compute it using the angle sum theorem.
A +B +C = 180°
A +85° +53° = 180°
A = 42° . . . . . . . . . . . . . subtract (85°+53°)
unknown side
Then side AC can be found from ...
AC/sin(B) = BC/sin(A)
AC = BC·sin(B)/sin(A) = 85·sin(85°)/sin(42°)
AC ≈ 126.547
The closest answer choice is 126.6.
