Find the value of x.
Round to the nearest tenth.

  C ≈ 22.1°

Step-by-step explanation:

The law of cosines formula is given. Solving it for C, we find ...

  C = arccos((a^2 +b^2 -c^2)/(2ab))

where a and b are the sides adjacent to the angle.

Then we have ...

  C = arccos((14^2 +19^2 -8^2)/(2·14·19)) = arccos(493/532)

  C ≈ 22.1°

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If you have a fair number of these to do, a spreadsheet is a useful tool. There are also triangle solver apps on the web or your local smart platform that will do this, too.

The interest rate would be 2.4%.

We start out finding the total amount he pays, including interest. 

78.40/month * 12 months * 5 years = $4704

We take off the amount of principal:
4704-4200 = 504

This is the amount of interest he pays.  Now we use the simple interest formula, I=prt:

504=4200(r)(5)

Multiply 4200 and 5:
504=21000r

Divide both sides by 21000:
504/21000 = 21000r/21000
0.024 = r
2.4% = r