An airplane leaves an airport and flies due west 150 miles and then 230 miles in the direction 7) S 39.67°W. How far is the plane from the airport at this time (to the nearest mile)?

The distance of the plane from the airport is 345.57 miles

Explanation:

The problem will be solved using the law of cosine which has the following formula

c ² = a² + b² - 2ab cosC

where  

c  is the side opposite to the angle  C

s² = (150)² + (230)² - 2(150) (230) cos (39.67⁰ + 90⁰)

s² = (150)² + (230)² - 2(150) (230) cos (129.67⁰)

s² = 22500 + 52900 + 44022

s² = 119,422

s = 345.57

Therefore, the distance of the plane from the airport is 345.57 miles

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