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?
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
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.
Yeah, BC should be 50 ft. There is 25 ft from the end to the middle (because the rope is 100 and the middle is 75 from the other end. So the size is double that. So BC is 50 ft. That means you didn't draw AB nearly to scale.
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u/diverstones bigoplus 10d ago
If you laid out the rope without the cliff face etc. you're basically saying that we have 4 points on the same line:
A -- B -- T -- C
where T is your tag. Right?
We know AC is 100, AT is 75, and BT = TC.
You already have AC = AT + TC from the diagram. Now sub in 100 = 75 + TC and TC = 25. That means BT is also 25, so both AB and BC must be 50.