A puzzle soved the old fashoned way but with Excel and trigonometry.
Two sticks 5m and 4m long are dropped in a well that is 3m diameter. At what height do the sticks cross ?
The easy trap to fall into is to assume that the angle at X is 90 Degrees, It's close but not exactly 90 Degrees. An estimate of the answer can be made using two sticks of equal length 4.5m that do meet at 90 Degrees for a much simpler calculations.
The two principles in the solution are :
Using Herons Law find the area of a gtriangle by knowings the lengths of it's sides and
Find the height of a triangle just by knowing the base length and area.
We can use each principle in turn to find the missing values on the route to the solution.
The difference between the estimate and the solution is about 94mm or 0.098m
