Math Problem

[MrControversial]

This is a problem straight out of a math book...lol. Not really, but it sounds like it. See, I get paid mileage for some network troubleshooting that I do. However, I failed to record milage from one point to the next. Using Map Quest I figured out that it was 21 mi. from point A to B and 8 mi from point A to C. However, I don't know the distance between points B to C. So I basically drew a triangle and I ended up with a obtuse triangle with the length of two sides known and the length of the last side unknown.

I'm almost ten years removed from high school geometry and I can't remember if there are any geometric or trigonometric formulas for finding the length of one side of the triangle when you know ONLY the length of two sides. For you math whizzes who may be fresher at this stuff than me, here's the math problem:

This obtuse triangle has sides AB= 21 and AC = 8. What is the length of side BC given no internal angles? Is this problem even solvable?

 

[Peter]

Anything between 13 and 29 miles, obviously.

 

[MrControversial]

I know it has to be a longer distance than from point A to B. Is there a forumla for solving the length of a side knowing the length of the first two sides.

 

[MrControversial]

Wait a minute. Check that, let's make this a right triangle, there's no reason for it not to be. In that case I can just use Pythagorean's Theorem!!!! Nevermind!

 

[MrControversial]

It was easier than I thought and the answer was reasonable too! I screwed up when I made it an obtuse triangle and not a right triangle. I used, aa + bb = cc and solved for bb. The length of side BC ended up being approx. 20 miles. Of course I round up so I don't jip myself out of money. They only pay us .28 to the mile anyways.

 

[Peter]

That's only correct for a right-angled triangle, which I doubt matches the map reality of your locations A,B,C. You always need three parameters to define a triangle - one side plus two angles, or two sides plus one angle, or three sides. Three angles doesn't define a triangle.

When you're only given two sides and no angle or 3rd side, then you can neither calculate nor draw the thing.

The extremes of your "triangle" are straight lines A-C-B and B-A-C, in which cases the distance B-C would be 13 and 29 miles respectively. "Proper" triangles yield any inbetween result for B-C.

 

[CycloWizard]

If you knew all the addresses, why didn't you just get directions in Mapquest from A to C?

 

[MrControversial]

I didn't know the address for one of them. Plus one goes west and one goes south so I can at least approximate a right triangle.

 

[bobsmith1492]

Obtuse triangle = law of cosines or sines.

 

[Calin]

If you have the point A and point B (latitude and longitude), you have a right triangle with one side being the longitude difference, and the other side the latitude difference. The latitude difference is like one nautical mile for every minute of latitude difference. The longitude difference is one nautical mile for every minute of longitude difference, multiplied with the cosine of the latitude that you are at

 

[NarcoticHobo]

Originally posted by: MrControversial
This is a problem straight out of a math book...lol. Not really, but it sounds like it. See, I get paid mileage for some network troubleshooting that I do. However, I failed to record milage from one point to the next. Using Map Quest I figured out that it was 21 mi. from point A to B and 8 mi from point A to C. However, I don't know the distance between points B to C. So I basically drew a triangle and I ended up with a obtuse triangle with the length of two sides known and the length of the last side unknown.

I'm almost ten years removed from high school geometry and I can't remember if there are any geometric or trigonometric formulas for finding the length of one side of the triangle when you know ONLY the length of two sides. For you math whizzes who may be fresher at this stuff than me, here's the math problem:

This obtuse triangle has sides AB= 21 and AC = 8. What is the length of side BC given no internal angles? Is this problem even solvable?

Maps usually have scales, how about you utilize the scale?

 

[bjamm2]

Originally posted by: bobsmith1492
Obtuse triangle = law of cosines or sines.

 

[Chubs]

Originally posted by: MrControversial
I didn't know the address for one of them. Plus one goes west and one goes south so I can at least approximate a right triangle.

BS... You stated you knew the distance AB and AC - you have to know the addresses for all three destinations or you wou'dn't be able to figure out one of the two legs you claim to know.