You are not logged in.
#1 2005-07-21 20:22:32
- bigpaully
- Novice
Offline
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
- Administrator
Offline
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
- Administrator
Offline
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
- Novice
Offline
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
if you have any questions please reply
Last edited by bigpaully (2005-07-21 22:30:56)
#5 2005-07-21 22:50:32
- MathsIsFun
- Administrator
Offline
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
#7 2005-07-21 23:28:07
- MathsIsFun
- Administrator
Offline
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
