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: 796 Thanks: 233 
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 
Newbie Joined: Oct 2017 From: UK Posts: 6 Thanks: 0  
October 30th, 2017, 11:31 AM  #6  
Newbie Joined: Oct 2017 From: UK Posts: 6 Thanks: 0  Quote:
 
October 30th, 2017, 11:34 AM  #7 
Newbie Joined: Oct 2017 From: UK Posts: 6 Thanks: 0  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  
Newbie Joined: Oct 2017 From: Redlands, CA Posts: 15 Thanks: 0  Quote:
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 Can anyone confirm this answer?  
November 11th, 2017, 10:46 PM  #9  
Newbie Joined: Oct 2017 From: Redlands, CA Posts: 15 Thanks: 0  Quote:
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: 3,110 Thanks: 855 
Why would the height of the balloon have anything to do with how big the balloon is?


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