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- anonymous

A plane is flying at an elevation of 20000 feet.
It is within sight of the airport and the pilot finds that the angle of depression to the airport is 23 degrees. find the distance between the plane and the airport.

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- amistre64

tan(23) = x/20000 is the ground distance; but do you want the actual distance from plane to airport?

- anonymous

The distance from the plane straight down to the earth is 20000 ft.
Draw a triangle with a plane on the top a line straight down (label it 20000 ft) and then draw a line to the right and at the end of it put the airport. Call that distance x

- amistre64

cos(23) = 20000/r
r = 20000/cos(23)

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- anonymous

amistre64 are you sure it is tan(23) I would think that you need the complement of the 23 degree angle?

- amistre64

we can use either angle, just recall that opposite over adjacent is the tangetnt.
since the planes angle is 23 degrees; we would do tan(23) = ground/height

- anonymous

But angle of depression is from the horizontal of the plane to the line of sight and this triangle is on the other side of that angle.
p -----------horizon
| \ 23 here
20000 | \
|.. ..\..........airport
Sorry... this is hard

- anonymous

Back up the airport to where the diagonal lines are.
Maybe I am wrong.. I thought that is what angle of depression was...

- amistre64

good, now we can simply take the tan(23) to get the ground/height
height*tan(23) = ground distance :)

- anonymous

Or angle of 23 from the airport up to the plane..
alternate interior angles

- amistre64

depression usually means looking down at something ..

- amistre64

you might be onto something there :)

- anonymous

Yes from the horizon down to where you are looking.
I agree with your cos(23) = 20000/x because you would be using the 23 at the bottom by the airport

- amistre64

in this inverted triangle we got tan(23) = height/ground distance.... I was turned over :)

- anonymous

the question is to find the distance from the plane to the airport which would be the cos(23) = 20000/x
p ----------
|\23
| \
| \
| \
|....23 \airport

- amistre64

r would be 20000/sin(23) since that makes it opp/hyp

- anonymous

OOPS you are correct...

- amistre64

im right AND wrong.... :)

- amistre64

lets just call it a tie :)

- anonymous

OK.. tie :-)
Wonder if btheuret is thinking... All I did was ask a question..
Hey btheuret take 20000/sin(23) and that is your answer.....

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