An airplane flies 200 km due west from city A to city B and then 270 km in the d

Question

An airplane flies 200 km due west from city A to city B and then 270 km in the direction of 31.5° north of west from city B to city C.

(a) In straight-line distance, how far is city C from city A? 424.12 km

(b) Relative to city A, in what direction is city C? 18.15 Correct: ° north of west

Please help with part A. The first time i got 406km and told me I was wrong but within ten percent of the correct answer. Then I got 424.12..Im not sure what im doing wrong. Please be specific with the answer. thank you

Explanation / Answer

a) d = sqrt [x2 + y2]

x = 200 + [270 * cos 31.5] = 430.21 km

y = 270 * sin 31.5 = 141.1 km

d = sqrt [430.212 + 141.12] = 452.75 km

b) tan phi = 141.1 / 430.21

phi = 18.15 deg

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