A plane is 120 miles north and 85 miles east of an airport. If the pilot wants to fly directly back to the airport, what angle should be taken?

Answer 1

The plane has to turn #125.31°# right to fly directly back towards the airport.

This would be on a bearing of #215°#

We can firstly map out how far north and east the pilot was from the airport, to find the angle to get back to the Airport.

see note below

#x = 54.69º#

Because the plane is flying due east, it has to turn 90º to face south, before it turns the extra #35.31º# to fly towards the airport.

#90° + 35.31° = color(blue)(125.31º)#

It actually turns through the exterior angle of the triangle :
#180-54.69° = 125.31°#

The question would be better if it asked for the bearing.
(Which is what a pilot would use)

Note: #tan^-1# is read as #"arctan:# (to find an angle from the ratio)

and is not the same as #1/tan# which would be #cot#

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Answer 2

The pilot should take an angle that corresponds to the inverse tangent of the ratio of the distances north and east of the airport. This angle represents the direction in which the plane should fly to return directly to the airport.

Using trigonometric principles:

Angle = arctan(North distance / East distance)

Given: North distance = 120 miles East distance = 85 miles

Angle = arctan(120 / 85)

Calculating the angle:

Angle ≈ arctan(1.4118) Angle ≈ 53.13 degrees

Therefore, the pilot should take an angle of approximately 53.13 degrees to fly directly back to the airport.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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