An airplane leaves an airport and flies due west 170 miles and then 240 miles in the direction S 69.50°W. How far is the plane from the airport (round to the nearest mile) ?.

We will use the Cosine Law:

c² = a² + b² - 2 a b cos C

∠ C = 90° + 69.50° = 159.50°

c² = 170² + 240² - 2 · 170 · 240 · cos (159.50°)

c² = 28,900 + 57,600 - 81,600 · (-0.9366722)

c² = 28,900 + 57,600 + 76,432.45

c = √ 162,932.45

c = 403.64 ≈ 404 miles

Answer:

The plane is 404 miles away from the airport.