An air traffic controller tells the pilot of an airplane flying due east to turn the plane so that it has a heading of 120 degrees east of north. What angle does the airplane turn and which direction is the plane now headed?
To find the angle that the airplane turns, and the new direction it is headed, we need to visualize the situation and use some basic trigonometry.
1. Start by understanding the initial direction of the airplane:
- The airplane is initially flying due east, which means its initial heading is 90 degrees east of north (since north is at 0 degrees).
2. Determine the angle the airplane needs to turn:
- The air traffic controller instructs the pilot to turn the airplane so that its heading is 120 degrees east of north.
- This means the airplane needs to turn an additional 30 degrees (120 - 90 = 30).
3. Determine the new direction the airplane is headed:
- Since the airplane initially had a heading of 90 degrees east of north, and it turned an additional 30 degrees, the new heading will be 120 degrees east of north.
So, the airplane turns 30 degrees to the right (clockwise) and is now headed 120 degrees east of north.