For any △ ABC, let the lengths of the sides opposite angles A, B, and C be a, b, and c, respectively.
The Law of Sines relates the sine of each angle to the length of its opposite side.
sin A/a=sin B/b=sin C/c
If we know the measures of the angles, we can use this law to find the missing side lengths opposite to these angles. To do so, we will start by drawing a diagram to illustrate the situation.
We know the measure of ∠ A and the length of its opposite side, BC. Also, we know the measure of the m∠ B. With this information we want to find the length of AC which is the side opposite to ∠ B. Let's write an equation to relate these pieces of information using the Law of Sines.
sin 42^(∘)/3 = sin 74^(∘)/b
Now, let's solve our equation!
