Imagine this: You're in a jungle, and somehow, you are required to measure. I doubt you'll need really 100% accurate measurements since you won't be doing architectural marvels in the middle of nowhere, and come on, I don't usually hear people bring their calculators into the jungle. So, here's a tip on how to estimate measurements, sorta.
Ok, let's say you need to measure the height of a tree, for no apparent reason. We can use trigo or similar triangles, the choice is up to you. But obviously, no one would choose trigo. Can you work out sin 64.5 without the aid of a calculator? No, I don't think so.
Anyway, here are the steps:
1) Get a
2) Get another person (Person B) to stand behind Person A. What Person B got to do is to bring his head down onto the floor (he got to sort of lie/kneel down, so it's kinda of a dirty job), and have him face the top of Person A's head.
3) Person B got to adjust his distance from Person A so that the top of the tree and the top of Person A's head line up in his line of sight.
4) Measure the distance from Person B's head to Person A's feet in steps.
What you have in the end should look something like this:
So, at this point, you should know these:
1) Distance of Person A from tree (CD)
2) Distance of Person B's head to Person B's feet (BC)
t=how tall Person A is
h=height of tree
Great, now we can use the so-called Similar Triangles to help us:
We know that:
BC/BD=t/h
By shifting the things around, we should get:
h=t (BD/BC)
So that means,
1) Take the distance of Person A from tree + distance of Person B's head from Person A's feet
2) Divide the answer by distance of Person B's head from Person A's feet
3) Multiply that by Person A's height
And that will give you the height of the tree.
This does not require a calculator. If at any case you can't use your head (maybe the fraction is too funky!), take a rock and count it on the floor. Actually, I don't even need to tell you this.
So, what are you waiting for, go try it!
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