Why is it so difficult to figure out how high Mount Everest actually is off the ground? I can think on many ways to figure it out, just off the top of my head, right now!
Send somebody up to the top with a parachute and a big ball of string. If they land, safely, that gives you the hypotenuse of a triangle. GPS will give the point from which they jumped. By measuring out from the base, vertically, below the jump off point, that will give you the base leg of a triangle.
In a right angle triangle, the tangent of the angle A, made where these two lines meet is equal to the opposite side divided by the hypotenuse. You want to know what the value is for that opposite side. So the equation becomes tan A multiplied by hypot is equal to the opp. side. The angle can be found by taking a protractor and measuring it where the base and hypotenuse meet and the tangent found by looking it up in tables.
Or for the more scientifically minded anorak, just use a lazer instead of the ball of string!! Who cares anyway??
There are much deeper valleys, which are inverted mountains, under the Sea, than any mountain above it!!
The Marianas Trench for one example.
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