Answer:
0.5 cm
Step-by-step explanation:
You are given angles B and C and side b, so you can put those values into the given equation:
sin(105°)/(2 cm) = sin(15°)/c
Multiply this equation by c·(2 cm)/sin(105°) and you get ...
c = (2 cm)·sin(15°)/sin(105°) ≈ 0.535898 cm
c ≈ 0.5 cm
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Comment on the given equation
When using the Law of Sines to find side lengths, I prefer to write the proportion in a form with the side length of interest in the numerator:
b/sin(B) = c/sin(C)
or
c/b = sin(C)/sin(B)
Using either of these forms, it is one step to find the value of c: Multiply the equation by the inverse of the coefficient of c.
c = b·sin(C)/sin(B)
