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## #1 2005-07-21 20:22:32

bigpaully
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### Angle of triangle with curved base

I am trying to figure out the angle of a triangle with a curved base of 3000km it is part of a circle that has a circumference of 24902km and a radius of 6378km. There is a line that bisects the triangle. Its length is 830km. I need the angle of the triangle that is opposite the 3000km curved side. I wish I could add a picture it would make things easier.   The triangle is outside the circle. Think of this problem as a satellite orbiting the earth.

## #2 2005-07-21 21:28:50

MathsIsFun

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### Re: Angle of triangle with curved base

[I removed the previous reply and banned the user]

It is just a *little* bit hard without a diagram!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #3 2005-07-21 21:40:05

MathsIsFun

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### Re: Angle of triangle with curved base

I caught the fact that you solved it yourself. Well done. But you did have the advantage of a diagram

The measurements sure do sound like this planet.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #4 2005-07-21 22:27:05

bigpaully
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### Re: Angle of triangle with curved base

here is a link to a diagram of the problem if anyone is still interested

Note: All I was given at the start of the problem was the swath coverage = 3000km (the curved area of the earth the satellite sees) and the altitude of the satellite = 830km.

http://img.photobucket.com/albums/v145/sealcock6/sat_swath_angle.jpg

Last edited by bigpaully (2005-07-21 22:30:56)

## #5 2005-07-21 22:50:32

MathsIsFun

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### Re: Angle of triangle with curved base

OK, well angle ARC is 360° × (3000/24902)

The angle ARE is half that.

The length RE is therefore cos(360° × (3000/24902) /2 ) × 6,378km

RE = cos(21.685°) × 6,378km = 5,927 km
AE = sin(21.685°) × 6,378km = 2,357 km

So distance ED = (6,378-5,927) + 830 = 1,281 km

We now know AE and ED, so the angle from that is:

tan-¹(2,357/1,281) = 61.5°, and you need to double that to 123°    --> ANSWER = 123°

There may be an easier way to get there, I just went about soloving triangles till I got there.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #6 2005-07-21 23:22:59

bigpaully
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### Re: Angle of triangle with curved base

right on. thats what i got well 122.88 degree. i needed to be a little more accurate.

## #7 2005-07-21 23:28:07

MathsIsFun

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### Re: Angle of triangle with curved base

Well, if we both got a similar answer it MUST be right.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

## #8 2005-07-22 00:06:18

Zach
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### Re: Angle of triangle with curved base

Either that or you're both wrong.

Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.