Answer:
C = 81.6 degrees
Explanation:
The formula for law of sines
sin A sin B sin C
-------- = ----------- = -------------
a b c
Looking at the diagram, we know A = 54, b = 7.4 and c = 15.8
not enough to use the law of sines
We will need to use the law of cosines
a^2 = b^2 + c^2 - 2ac cos A
Using the law of cosines, we can calculate the length of a
a^2 = 7.4^2 + 15.8^ -2*7.4*15.8 cos 54
a^2 = 54.6+249.64-233.84cos54
a^2 =166.7922966
a = 12.921
Now we can use the law of sines to find C
sin 54 sin C
-------- = -------------
12.921 15.8
Using cross products
15.8 * sin 54 = 12.921 * sin C
Divide each side by 12.921
15.8 /12.921 * sin 54 = sin C
Take the arcsin of each side
arcsin (15.8 /12.921 * sin 54) = arcsin (sin C)
arcsin (15.8 /12.921 * sin 54) = C
C = 81.6 degrees