City A is 350 miles due south of City B. City C is 500 miles due east of City B. What is the measure of ??C to the nearest degree

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Answer 1

tanC 350/500 = 0.7 = tan 35

 

thus the angle C is about 35°

Answer 2

If this were to be drawn, it would be a right triangle with the 90 degree angle at B. the lengths would be 350 between B and A and 500 between B and C.

 

You could use tan inverse function on your calculator because 350 is on the opposite of angle C and 500 is adjacent. Both are known. Tan^-1(350/500) is 35 degrees.