Notice that the arc measure between two consecutive hours on the clock is 30^(∘).
Diagram:
The Distance Between Pilot A and the Object: ≈ 462 ft
Practice makes perfect
We are asked to draw a diagram showing the possible locations of the two planes and the object given the references to the dial of a clock. Then we will use our diagram to find the distance between Pilot A and the object. Let's start with the first part!
Drawing a Diagram
We are asked to suppose that two pilots flying in the same direction spot the same object. First, we know that Pilot A reports the object at 12 o'clock.
Next, we are given that Pilot B reports the object at 2 o'clock and at the same time Pilot A reports seeing the other airplane at 9 o'clock.
Now we are given that the planes are 800 feet apart and we want to evaluate the distance between Pilot A and the object. Let d represent this distance.
Recall that in a 30^(∘)-60^(∘)-90^(∘) triangle the length of the longer leg is sqrt(3) times the length of the shorter leg. Using this information, we can write an equation.
800= dsqrt(3) ⇓ d=800/sqrt(3)≈ 462
Pilot A is approximately 462 feet from the object.
