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?

1 Answer
May 21, 2017

Answer:

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

This would be on a bearing of #215°#

Explanation:

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.

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(not to scale)

#x = tan^-1 (120/85)" "#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#