If in a triangle, measure of angle a is 71 degrees, measure of angle b is 42 degrees, and bc= 8, find ac to the nearest hundredth.

Length BC is opposite of angle A and AC is opposite of angle B. 

Since we know one set of opposite angles and lengths and looking for the length where we know the opposite angle, we can use law of sines: 

a / sin(A) = b / sin(B) 
8 / sin(71) = b / sin(42) 
b sin(71) = 8 sin(42) 
b = 8 sin(42) / sin(71) 
b ≈ 5.66 units (rounded to 2DP)

With a continuous thought process.