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Flights 204 and 317 are both approaching Hartsfield Atlanta International Airport from directions directly opposite one another and at an altitude of 2.5 miles. The pilot on flight 204 reports an angle of depression of 17 degrees 47 minutes to the tower, and the pilot on flight 317 reports an angle of depression of 12 degrees 39 minutes to the tower. Calculate the distance between the planes.

Respuesta :

mhanifa

Answer:

  • 19.26 miles

Step-by-step explanation:

Refer to attached picture. Not to scale.

The picture explains all the given parameters.

We need to find the distance d, which is the sum of x and y.

First convert minutes to degrees:

  • 47 min = 47/90 deg = 0.52 deg
  • 39 min = 39/90 deg = 0.43 deg

Find x:

  • x/2.5 = cot (17.52°) ⇒ x = 2.5*3.1677 ≈ 7.92 mi

Find y:

  • y/25 = cot (12.43°) ⇒ y = 2.5*4.5369 ≈ 11.34 mi

The distance between the planes:

  • 7.92 + 11.34 = 19.26 mi
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