Question

Use the law of sines to find the length of side c.
C
be
41.59
37
42°
А
С
CD
O A. 36.64
B. 54.94
C. 37
37 36

Answer 1

Without the calculator let's just estimate that .5/42 = 1.2% change in the angle; we reduce the length a=37 by 1.2% to get 37×.988=36.556.  That's probably good enough to choose A.

Let's do it the way they want.

$\dfrac{\sin C}{c} = \dfrac{\sin A}{a}$

$c = \dfrac{a \sin C}{\sin A} = \dfrac{37 \sin 41.5}{\sin 42} = 36.6400$

Answer: A

Estimate worked.  Sine is approximately linear when the range is small enough.