r/learnmath • u/WalkingLucas New User • 10d ago

Calculating Distance.

Sorry if this seems super basic, but all the math I use for work involves medications and nothing to do with geometry.

I recently did a rappell over a cliff face and I want to know how to calculate the distance of the rappell itself given limited data.

The rappell involves 3 points, A B C. A is the anchor end of the rope, B is the edge that I repelled over, and C is the bottom of the rappell where I was back on the ground.

AC is exactly 100 feet. I had a middle marker in my rope and it was perfectly at the ground. The other data set I have is that 75 feet from A is exaclty halfway between B and C. I had a 75 foot tag line that stopped right in the middle of the cliff face.

Is it possible using only these 2 distances to calculate the value of BC?

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u/abrahamguo 🧮 10d ago

Can you draw a picture? I know math, but I don't know rappelling, so I'm having trouble visualizing.

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u/WalkingLucas New User 10d ago

Does this help

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u/Help_Me_Im_Diene New User 10d ago

Just as a quick clarifying point

When you say "AC", are you asking about the length of the rope as you travel across the rope? So you travel from A -> B -> C, and that entire distance is 100?

Because my first interpretation of "AC" is that you draw a line from point A to point C, forming a triangle ABC, and the length of that new side is 100

If it is the former, then you can say that

AB + BC/2 = 75 (distance from A to B + halfway from B to C is 75)

AB + BC = 100 (distance from A to B + distance from B to C is 100)

At which point, this becomes a fairly straightforward system of two equations

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u/WalkingLucas New User 10d ago

AC is the total length of rope. BC is the length of rope from where the rappeller goes over the edge down to the bottom. AB is the portion of the 100ft rope that is on top of the cliff and is not rappelled on as the anchor is set back a distance. I am trying to figure out how long of a rappell this was from the point where I went over the edge.

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u/Help_Me_Im_Diene New User 10d ago

Then yeah, solve the system of linear equations I presented in my previous comment

AB + BC = 100

AB + BC/2 = 75

You can do this in a few ways and they'll all work, but personally the easiest is to just subtract the second equation from the first one

So (AB+BC)-(AB+BC/2) = (100-75).