## Finding rocket's distance at various angles after launch

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
JDC
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### Finding rocket's distance at various angles after launch

Hi, I'm new here but I haven't been in school for many years and recently I've been trying to remember some trig.

Something I find strange is plotting angles and calculating distances with known values.

I was hoping someone could help me remember, or rather, re-educate me on the following.

I've attached a picture.

45 degrees is a much simpler thing to plot since for ever x there is an equal y, 1,1 2,2 4,4 99,99 etc..

But when it comes to angles like 26.57 the plotting just doesn't seem correct on graph paper.

Essentially I can really trying to solve for something that looks like this. (I promise this is NOT homework)

Thanks to anyone in advance for assisting.

buddy
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### Re: Finding rocket's distance at various angles after launch

I think you've got like this:

Code: Select all

```rocket path: l *. v a / | ` . i u / | ` . e n / |h ` . w c /45* | 10* ` . e h *---------*------------------* r |<===========150============>| ```
Since the triangle on the launch side is 45 degrees then the base is h too. Then the base of the viewer's triangle is 150-h. So do the tangent of the 10 degrees & make it equal to h/(150-h). Solve for h & subtract this from 150 to get distance A. Do the same set-up for B & C.

JDC
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### Re: Finding rocket's distance at various angles after launch

Great, thanks, I'm not sure what Tangent is, I've seen it many times but never had to use it. I'll look it up, thanks for your help.

JDC
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### Re: Finding rocket's distance at various angles after launch

Lets say I know
1) The distance between the Rocket and the Observer
2) I know the Angle of the Rocket
3) I know the angle of the observer.

How do I calculate the horizontal distance where the angles meet?
I don't care to determine the distance the angles are, just the bottom length.

What I need to do is to be able to translate that into Cartesian Coordinates as well, but 1 step at a time I guess, thanks a lot. (please)

nona.m.nona
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### Re: Finding rocket's distance at various angles after launch

How does your new situation differ from the original, other than in that the angle of launch is now variable?

JDC
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### Re: Finding rocket's distance at various angles after launch

I suppose it isn't but I noticed that since it was 45 degrees you mentioned h was the same... and I didn't want to assume anything.

I'm trying to work the formula out on Excel right now, so if you had any time to reply with an example input values and the functions to use that would help me most. I know sometimes working things out for someone isn't always considered a great learning experience for the receiver but in my case my lack of time in the evenings doesnt allow me a very large window of opportunity.

Thanks again

buddy
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### Re: Finding rocket's distance at various angles after launch

Code: Select all

```rocket path: l *. v a / | ` . i u / | ` . e n / |h ` . w c /x* | 10* ` . e h *---------*------------------* r | d | |<===========150============>| ```
if its some other x-degree angle then do tan(x)=h/d & tan(10)=h/(150-d). then solve the system for h & d (or just d really since thats what you need).

JDC
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### Re: Finding rocket's distance at various angles after launch

Ok, so what I do know are the three angles and the distance along the bottom.

With those 4 items (3 angles and length across the bottom) are you saying I need to first solve for the height/alt then I can determine the length of each triangle?

buddy
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### Re: Finding rocket's distance at various angles after launch

no. you can do like i showed & then solve for d. you dont have to solve for h too.

JDC
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Joined: Mon Nov 25, 2013 2:46 am
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### Re: Finding rocket's distance at various angles after launch

Ok, I'll try...

I found this site, I'm not sure if I'm suppose to use Radians or Degrees. I assume degrees?

http://www.rapidtables.com/calc/math/Tan_Calculator.htm