My Math Forum Triangulation

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 October 28th, 2017, 10:29 AM #1 Newbie   Joined: Oct 2017 From: UK Posts: 6 Thanks: 0 Triangulation Hi, I am having difficulty with this question. I can't seem to get anywhere near the right answer so I think I am misunderstanding something. I am really interested in the step by step working out. Last edited by skipjack; November 12th, 2017 at 06:37 AM.
 October 28th, 2017, 11:34 AM #2 Newbie   Joined: Oct 2017 From: Redlands, CA Posts: 15 Thanks: 0 I'm no expert but here's the picture I drew which is what I would start from. Is this the correct approach guys?Trig problem.jpg
 October 28th, 2017, 01:20 PM #3 Newbie   Joined: Oct 2017 From: UK Posts: 6 Thanks: 0 I think I have the right idea. That there are three triangles. The one created by the bearings and two created by the elevations. I work out the edges of bearings triangle first. As it shares edges with the elevation triangles, it helps me with figuring out the height of the balloon (which is a shared edge of the elevations triangles). But some help would be great. Last edited by skipjack; November 12th, 2017 at 06:39 AM.
 October 28th, 2017, 01:43 PM #4 Senior Member   Joined: Jun 2015 From: England Posts: 887 Thanks: 266 There are 4 triangles. The 3D diagram looks like a wedge of cheese, with two sides, a base and a sloping face, all triangular. Are you assuming the ground is completely flat? Last edited by studiot; October 28th, 2017 at 02:29 PM.
October 30th, 2017, 11:30 AM   #5
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 Originally Posted by studiot There are 4 triangles. The 3D diagram looks like a wedge of cheese, with two sides, a base and a sloping face, all triangular. Are you assuming the ground is completely flat?
Yes, ground is flat.

October 30th, 2017, 11:31 AM   #6
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 Originally Posted by JPow I'm no expert but here's the picture I drew which is what I would start from. Is this the correct approach guys?Attachment 9274
You would then use the law of sines to work out one of the edges? given you have 3 angles and 1 side.

October 30th, 2017, 11:34 AM   #7
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 Originally Posted by studiot There are 4 triangles. The 3D diagram looks like a wedge of cheese, with two sides, a base and a sloping face, all triangular. Are you assuming the ground is completely flat?
Am I right in saying you can ignore the sloping face of the cheese wedge? Since you can use the base triangle to work out an edge of one of the side triangles?

Last edited by skipjack; November 14th, 2017 at 04:22 AM.

November 11th, 2017, 10:12 PM   #8
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 Originally Posted by mathishardbutfun You would then use the law of sines to work out one of the edges? given you have 3 angles and 1 side.
Yes, law of sines is the right approach. Did you get it solved?

From the first picture you would find the top missing angle by knowing the 3 will add to 180.

Then use law of sines to solve for an additional side and then for the height.

Here's what I got:
IMG_0532.jpg

November 11th, 2017, 10:46 PM   #9
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 Originally Posted by JPow Yes, law of sines is the right approach. Did you get it solved? From the first picture you would find the top missing angle by knowing the 3 will add to 180. Then use law of sines to solve for an additional side and then for the height. Here's what I got: Attachment 9293 Can anyone confirm this answer?
Reading the question again I think what I did was only half the problem. You would do all the calculations again using the elevation angles and then subtract from the answer using the bearings to get the actual height of the balloon itself.

Then I end up with 2.28 km. Pretty big balloon huh? Not sure if that's right.

 November 12th, 2017, 04:00 AM #10 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Why would the height of the balloon have anything to do with how big the balloon is?

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