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

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

The plane is 404 miles away from the airport.