# math

lets say you have a tree or a flagpole. Describe how you would measure this object using right angled triganometry

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1. Is the sun shining? If so, you could take a one-meter ruler, place it vertically on the ground, mark both the point on the ground where you placed the ruler and the point where the end of its shadow is, then take the ruler away. Next, use the ruler to measure both the length of the shadow you've just created by the ruler itself, and then the length of the shadow created by the flagpole. The ratio of the flagpole shadow length to the length of the shadow of the ruler should give you the height of the flagpole in meters. (Sherlock Holmes did something very similar in "The Musgrave Ritual" to determine how long a shadow must have been cast of a tree that was no longer there, given that the height of the tree before it was felled was known.)

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2. I think i need to explain this method using SOH CAH or TOA

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3. No problem - but you'll still need to be able both to measure a distance and to calculate an angle. Measure the distance between the bottom of the flagpole and a point some convenient distance away - it doesn't really matter how far, but say it's Y meters. Now work out the angle of the top of the flagpole from where you're standing. I don't know if you're going to do that with a sextant or something, but you need to know that angle: call it A. Then if X is the height of the flagpole, you know that (X/Y) is the tangent of A, i.e. X/Y = tan(A). So X = Y tan(A), so you're using TOA.
For example, if you're standing 10 meters away from the flagpole, and A = 60 degrees, then tan(A) = 1.732 (you'll get that from a set of tables), so the height of the flagpole is 10 x 1.732 = 17.32 meters.
One last thing: strictly speaking, you'd need to add YOUR height to the calculation. If you're standing up, you'll be getting on for two meters above the ground - so unless you're lying on the ground when you work out the angle above the horizontal of the top of the flagpole, you'll need to allow for that too.

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