Question

Charlie is at a small airfield watching for the approach of a small plane with engine trouble. He sees the plane at an angle of elevation of 32. At the same time, the pilot radios Charlie and reports the plane’s altitude is 1,700 feet. Charlie’s eyes are 5.2 feet from the ground. Draw a sketch of this situation (you do not need to submit the sketch).

Find the ground distance from Charlie to the plane. Type your answer below. Explain your work.

Answer 1

Let's draw it out!

Answer 2

X is essentially the ground distance here. So we must find x.
This problem is just a simple case of trig.
Since it is ground distance, it shoudl be the same as the eye level in all honesty. His eye level is parallel to the ground

Answer 3

our trig functions to use are from
Sin (SOH)
Cos (CAH)
Tan (TOA)
In this case, we are given the angle, and the side opposite of it, while we are trying to find the adjacent side to it. Therefore, we will use Tan.

Now, before we plug in all the values, let us take note that in the picture, I have drawn it to Charlie's perspective from what HE SEES.
He is 5.2 ft above the ground, and the altitude is 1700, the picture has a line from his eye level. So we need to subtract 5.2 from 1700 to be accurate. Else, our whole problem gets messed up.
NOW LETS PLUG IT IN!!
We are using TAN
So,
Tan(angle)=opp/adjacent
Tan(32)=(1700-5.2)/adj
We are trying to solve for the adjacent side now
So...
mult adj on both sides
tan32adj=((1700-5.2)/adj)(adj)
tan32adj=1700-5.2
Mult by tan32 on both sides to make adj be alone
adj=(1700-5.2)(tan32)
Plug this into your calculator, and you get your answer
:)
Hope this helped! Happy New Year to ya :) x
KC