FINDING THE BEARING OF AN AIRCRAFT. (Trig)

[LisaH2016]

I am having trouble understanding how the book got the answer to this problem:

A DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40degreesE. After flying for 1/2 mile, the pilot requests permission to turn 90 degrees and head toward the southeast. The permission is granted. After the airplane goes 1 mile in the direction, what bearing should the control tower use to locate the aircraft?

My work: 1/2 is the adjacent to the 40 degrees. Then the 1 mile is the opposite. I used TAN theta = opposite/adjacent. I submit the values in and i got

TAN theta = 1/(1/2) = 2. Then isolating theta angle it becomes Theta = TAN inverse (2) = 63.43

I first subtracted 40 degrees and got 23.43. and then I added 40 to 63.43 = 103.43. the book says the answer is 76.6. HOW did they come up with that answer.

Please explain in detail. Thanks.

Lisa.

 

[wjm11]

I am having trouble understanding how the book got the answer to this problem:

A DC-9 aircraft leaves Midway Airport from runway 4 RIGHT, whose bearing is N40degreesE. After flying for 1/2 mile, the pilot requests permission to turn 90 degrees and head toward the southeast. The permission is granted. After the airplane goes 1 mile in the direction, what bearing should the control tower use to locate the aircraft?

My work: 1/2 is the adjacent to the 40 degrees. Then the 1 mile is the opposite. I used TAN theta = opposite/adjacent. I submit the values in and i got

TAN theta = 1/(1/2) = 2. Then isolating theta angle it becomes Theta = TAN inverse (2) = 63.43

I first subtracted 40 degrees and got 23.43. and then I added 40 to 63.43 = 103.43. the book says the answer is 76.6. HOW did they come up with that answer.

Please explain in detail. Thanks.

Lisa.

Lisa, your answer (and Denis' calc for angle NAC = 103.43) is the correct answer. NAC is the bearing angle.

Whoever did the calc in the book lost a sign somewhere. 76.6 is 13.4 degrees north of due east, and the plane's position is 13.4 degrees south of due east.

"Bearing angles" have some similarities and some dissimilarities from what you've already learned using an xy (Cartesian) plane. In Cartesian coordinates, we define a positive angle starting from the horizontal (positive x) direction and opening up counterclockwise.

Bearing angles are related to navigation, and ancient navigators naturally decided due North was a good place to start counting from (due to the use of the pole star, Polaris, at night and magnetic compasses during the day). And instead of making counterclockwise be the positive angle direction, they chose clockwise (likely because that is the direction a shadow on a sundial in the northern hemisphere moves).

So to find a bearing angle, one starts by facing North, then rotates clockwise until they are facing the object of interest. The angle you've rotated is the bearing angle.

Hope that helps.

 

[LisaH2016]

thanks for both responses! It helped me understand alot better. i was so lost. Thanks ALOT