Question

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)?.

Answer 1

C=403.6489

Explanation:

A= 170, B= 240 angle C= 69.5+90=159.5

C= the distance from the plane to the airport.

Answer 2

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.