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
We can use this law to find the missing angle. To do so, we will start by drawing a diagram to illustrate the situation.
We know the measure of ∠ B and the length of its opposite side, AC. Also, we know the length of BC. With this information we want to find m∠ C. To do that, we will first find m∠ A, which is the angle opposite to BC and then use he Triangle Angle Sum Theorem. Let's write an equation to relate these pieces of information using the Law of Sines.
sin 120^(∘)/10 = sin ∠ A/8
Now, let's solve our equation!
To find m∠ A, we will use the inverse operation of sin, which is sin ^(- 1).
sin ∠ A=sin 120^(∘)/10 * 8
⇕
m∠ A=sin ^(- 1)(sin 120^(∘)/10 * 8)
Finally, we will use a calculator.
Now, let's recall that the Triangle Angle Sum Theorem tells us that the measures of the interior angles of a triangle must add to 180. Knowing the measures of two angles, we can create an equation to solve for ∠ C.
