Finding the Magnitude of Displacement in a Mountain-Climbing Expedition

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The discussion focuses on calculating the magnitude of displacement between two camps, A and B, in a mountain-climbing expedition using Pythagorean theorem principles. The user initially estimates the horizontal distance between the camps as 8400 meters and calculates the hypotenuse (displacement) as approximately 9724.71 meters. The final displacement is derived by subtracting the vertical distance from the hypotenuse, resulting in a value of 6524.71 meters. The conversation emphasizes the application of basic trigonometric concepts to solve real-world problems in mountaineering.

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I am in no way trying to ask you to do this problem for me, i just need a little guidance, like where do i start and i feel like i should be able to figure out the rest. My textbook uses examples but when i the questions come up it looks completely different so i don't know where to start.

A mountain-climbing expedition establishes two intermediate camps, labeled A and B in the drawing, above the base camp. What is the magnitude r of the displacement between camp A and camp B?

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My thoughts about the question were (its hard to explain except on paper but ill try to show you what i thought to do): Displacement = (triangle)R = r - r(sub 0). I assumed that the distance from camp A and B is 8400 ( (Base Camp to camp B) - (Base Camp to Camp A). Then i made a line from the bottom point of the line under camp A diagonally up to camp B and that is the r(sub 0) line. I used a^2+b^2=c^2 to find out that r(sub 0) is 9724.71 and then i used 3200m as r and i did r - r(sub 0) = 6524.71 meters. But i have not clue if i did any of that right?? If you could let me know i would appreciate it.
 
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This is basically pythagoras' theorem. You have found the horizontal distance between the camps to be 8400m. The difference in height between the two will be the other side then r will be the hypotenuse which you can work out.
 

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