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The "number" is correct for your solution to part one of the first problem, but I don't like what you have written.

The resultant vector is

(120 + 200COS52, 200SIN52)= (243.132, 157.602)

The magnitude of this vector is

Sqrt(243.1322 +157.6022) = 289.744

The angle measurement of BAC is 52 degrees and the vector AD is the resultant vactor. The angle you want is BAD and you know the lengths of the sides of the triangle BAD so you can find the angle you need using the Law of Coaines.

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