Question

A plane is flying at an elevation of 34000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 14 degrees.Find the distance between the plane and the airport.Find the distance between a point on the ground directly below the plane and the airport.

Answer 1

This is problem states an angle of depression from the pilots point of view so we know that the angle of depression will be at the plane

Answer 2

I have a clarifying question. Is the point below the plane below the airport as well?

Answer 3

oh wait I'm dumb

Answer 4

Since we want to find a point below on the ground relative to a point below the plane then we know we also have a 90 degree triangle and we can use the or trig laws

Answer 5

We want to solve the opposite side to the angle while only knowing the side adjacent to the angle

Answer 6

Use tan?

Answer 7

So a relationship for Adjacent side and Opposite side would be\[\tan \theta = Opposite/Adjacent\] and we want to solve for the opposite side

Answer 8

Correct!

Answer 9

Tan14=x/34000

Answer 10

Correct!

Answer 11

Now all you have to do is get the x by itself and solve the function

Answer 12

I got 8477.152097 but it's saying that is incorrect

Answer 13

If it asks you to round to any significant figures you should do so

Answer 14

Usually they ask to round to a certain amount of decimal places or to the nearest whole number

Answer 15

Whoops we might have solved for the wrong side?

Answer 16

On my webwork it isn't asking for anything specific but I tried rounding to the whole number like you said and it's still incorrect

Answer 17

Would it be cosine?

Answer 18

would it be 8500 feet? I am not seeing the error yet if there is one

Answer 19

No, it's still saying incorrect

Answer 20

Oh i see there is actually 2 questions in 1 so first is the distance between the plane and the airport and then from the ground to the airport. We solved the 2nd question.

Answer 21

The plane to the airport would be the hypotenuse so knowing the angle with the adjacent side and hypotenuse which trig law could we use?

Answer 22

I tried plugging it into the second question and it also said incorrect

Answer 23

Cosine??

Answer 24

No way! That can't be maybe you have to solve for the first 1 and the second at the same time

Answer 25

That's my reaction I've tried plugging it in over 20 times

Answer 26

Correct So we would have:\[\cos(14) = 34,000\x]

Answer 27

Solving for x would give us\[x = \frac{ 34000 }{ \cos(14) }\]

Answer 28

What if that answer is incorrect

Answer 29

Try plugging them both in at the same time with at least 2 decimal places at the end

Answer 30

It still says incorrect

Answer 31

The angle of depression should mean that the angle is -14 degrees i believe but that doesn't change the answer for the cosine

Answer 32

And it seems it would make the tan negative which isnt right either so I am confused do you think there is a mistake in the numbers you read?

Answer 33

I tried it again and got the same answers

Answer 34

Only way i see this problem that it might actually be shaped like this instead

Answer 35

To find a point below the ground to the airport would then look like this

Answer 36

The triangle u drew before that one answered my second question !

Answer 37

so for the distance of the airport to the ground we can use \[x=\frac{ \tan(76) }{ 34,000 }\]

Answer 38

Which 1? and which question?

Answer 39

The upside down triangle answered, Find the distance between a point on the ground directly below the plane and the airport.

Answer 40

Awesome so it must be the same to find the distance between the airport and the plane. Which function did you use for the second problem?