Trig- asap! use either the law of cosines or the law of sines to find the measure of angle c

C = 81.6 degrees

Step-by-step 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

the correct answer is d

hope this