Question Video: Finding an Angle Between Two Bearings Mathematics

A plane flies on the bearing. The control tower told the pilot to fly due west toward the airport. Which of the following is the angle the pilot should turn through? [A] 137° clockwise [B] 90° counterclockwise [C] 270° counterclockwise [D] 133° counterclockwise [E] 223° clockwise


Video Transcript

A plane flies on the bearing shown. The control tower told the pilot to fly due west toward the airport. Which of the following is the angle the pilot should turn through? Is it (A) 137 degrees clockwise, (B) 90 degrees counterclockwise? Is it (C) 270 degrees counterclockwise, (D) 133 degrees counterclockwise, or (E) 223 degrees clockwise?

We’re given a path of a plane in our diagram and we’re told that, at some point, the control tower tells the pilot to fly due west. We know that relative to the north line, to travel west, we’d move to the left on our diagram. And so, we see that the plane is going to travel left on our diagram. Now, given the direction the plane is traveling, there are two ways the pilot could achieve this. Firstly, they could travel in a counterclockwise direction as shown. A slightly longer route will be to travel in a clockwise direction. Let’s begin by looking at the counterclockwise direction since this is slightly shorter.

Now, there are a number of ways we can find this angle. One way is to add a north line at the location of the pilot. We then know the two north lines in our diagram are parallel. So, we can add 43 degrees here, since we know that corresponding angles are equal. We also know that the north line and the west line are perpendicular. They meet at an angle of 90 degrees. And so, we can calculate the angle that the pilot turns through by adding 90 and 43. 90 plus 43 is 133 degrees. And so, the pilot could turn 133 degrees counterclockwise. And that’s option (D).

But remember, we said that the pilot could have turned in the opposite direction. They could have traveled in a clockwise direction. So, how could we have calculated this angle? Well, by extending the west line and recalling that the north line and west line are perpendicular, we can draw a right-angle triangle, as shown. We know that angles in a triangle sum to 180 degrees. So, we can find the third angle in this right-angle triangle by subtracting 90 and 43 from 180 to get 47 degrees.

We know that angles on a straight line sum to 180 degrees. And so, had the pilot turned on a clockwise direction, the angle would’ve been calculated by adding 180 to 47 to get 227 degrees. And so, this isn’t one of our options. But we could have said that the pilot needed to turn on an angle of 227 degrees clockwise.

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