PLEAAAAAASE HELP!!!!!!! will give medal!

Question

akashdeepdeb · Answer

Use trigonometry here!
Tan x = 9000/6000

anonymous · Answer

I tried that and still didn't get the right answer @AkashdeepDeb

debbieg · Answer

Do you know what to do with 

$\Large \tan(x)=\dfrac{9000}{6000}$    to find x?

anonymous · Answer

I divide 9000/6000 right?

debbieg · Answer

That will reduce the fraction that tan(x)= but wont tell you x.

anonymous · Answer

I don't understand? How do i solve it?

debbieg · Answer

Sorry, had a phone call.

You have $\Large \tan(x)=\dfrac{9000}{6000}$ which reduces, so just for ease let's do that, and you get

$\Large \tan(x)=\dfrac{3}{2}$

right?

debbieg · Answer

Now, you are looking for the ANGLE, x, that solves $\Large \tan(x)=\dfrac{3}{2}$, right?

That is, whatever (acute) angle makes that true, is the angle of depression that you are looking for, right?

Does that much make sense?

anonymous · Answer

The first part makes sense but i still dont follow on the second part

debbieg · Answer

OK, tell me which part doesn't make sense. I kind of thought that was just one part... lol. Do you understand how @AkashdeepDeb  set up the equation 

$\Large \tan(x)=\dfrac{9000}{6000}$
from the problem description and diagram?

(I'm assuming so, since you said you already had that much.)

debbieg · Answer

And then, do you understand that I simply reduced that fraction to make it

$\Large \tan(x)=\dfrac{3}{2}$

which, strictly speaking, wasn't really necessary but is just easier to look at and type. :) And it's equivalent, anyway, so it doesn't hurt anything to do so.

anonymous · Answer

okay yes i follow, i just dont understand how i get x

debbieg · Answer

OK, that's fine, we're going there next. :)

debbieg · Answer

So we have that $\Large \tan(x)=\dfrac{3}{2}$. Think about what that MEANS.

It means that x (the angle we're looking for) is some angle that has, as the value of its tangent, the number 3/2.

That is, when the tangent function takes our unknown angle x as an "input", it gives us the number 3/2 as an "output".

Good so far?

anonymous · Answer

yes

debbieg · Answer

Now what we want is to find our x. So what we NEED is something that turns that around.

We need something that lets us "input" a tangent VALUE, and takes it and gives us an "output" of the ANGLE MEASURE that HAS THAT as its tangent value.

debbieg · Answer

Do you know anything like that?

Maybe.... say..... another function? That flips the tangent function around like that?

anonymous · Answer

no, the lesson that was supposed to teach me how to do this was only 3 pages long and very vague. So i don't know how to do this at all

debbieg · Answer

Are you sure it doesnt mention either the arctan function 

$\Large y=\arctan(x)$

Or, it might refer to it as the "inverse tangent function"

$\Large \tan^{-1}(x)$

They are the same thing, just can be called by either name.

anonymous · Answer

Deffinitley did not see anything about that... ive re-read the entire lesson atleast 6 times trying to firgure it out on my own, ive even tried the previous lesson, and the one after it

debbieg · Answer

But if not - that's ok - then all that matters is that inverse tangent function is the INVERSE of the TANGENT function.

As for any function and inverse, it "flips around" the inputs and outputs. so in 

$\Large y=\tan^{-1}(x)$

Your INPUT x is a TANGENT VALUE. Then your OUTPUT y is an ANGLE MEASURE. You can do this in radians OR degrees, same meaning, and here you obviously want degrees.

There is also one other "technical" restriction on the inverse trig functions, and for tangent that is that it will always give you an angle between -90* and 90*. The reasons for that are not important here, and won't affect your answer since your angle is obviously between 0* and 90* (I just didn't want to be remiss in mentioning it). :)

debbieg · Answer

So, your calculator should have a button that looks like that function

$\Large [\tan^{-1}(x)]$

On a TI-83 it's a "2nd" function, just above the [TAN] button.

So to find the angle x such that

$\Large \tan(x)=\dfrac{3}{2}$

you simply need to evaluate

$\Large \tan^{-1}(\dfrac{3}{2})$

which is, by the definition of the inverse function, "the angle between 0* and 90* that has a tangent value of 3/2".

debbieg · Answer

(Make sure your calculator is in degree mode, so that it gives you the output in degrees. if you are in radian mode, it will give you x in RADIANS, not in DEGREES.)

anonymous · Answer

@DebbieG I got 56.31! Is that right?

debbieg · Answer

Yessiree!  :)

debbieg · Answer

But what I REALLY hope is that you have a bit of an understanding about the inverse function, now. :) It's very handy in trig! :)

anonymous · Answer

omg thank you so much! That makes so much more sense. My calculator was in 1st degree mode when i was trying to solve

debbieg · Answer

You're welcome, happy to help. :)