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An airplane flies 200 km due west from city A to city B and then 355 km in the direction of 27.5° north of west from city B to city C.(a) In straight-line distance, how far is city C from city A?(b) Relative to city A, in what direction is city C?(c) Why is the answer only approximately correct?

Question

An airplane flies 200 km due west from city A to city B and then 355 km in the direction of 27.5° north of west from city B to city C.

(a) In straight-line distance, how far is city C from city A?
(b) Relative to city A, in what direction is city C?
(c) Why is the answer only approximately correct?
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Step 1

Draw the diagram. Here, AB is the distance between the cities A and B, BC is the distance between the cities B and C and AC is the distance between the cities A and C.

A
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A

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Step 2

(a) Using cosine law for triangle vector addition, the straight line distance between the cities A and C is:

AC (AB)(BC +2(AB)(BC) cos
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AC (AB)(BC +2(AB)(BC) cos

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Step 3

Substitute 200 km for AB, 355 km for BC and 27.50 for &the...

AC (200 km) +(300 km) +2(200 km) (300 km) (cos 27.5°)
AC 486.25 km
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AC (200 km) +(300 km) +2(200 km) (300 km) (cos 27.5°) AC 486.25 km

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