Two Fences, a Distance of D = 16 Feet Apart

question 121

Essay

Two fences, a distance of d = 16 feet apart are to be constructed so that the first fence is a height of h = 2 feet high and the second fence is higher than the first. What is the length of the shortest pole that has one end on the ground, passing over the first fence and reaches the second fence? See figure.

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Definitions:

Chebyshev's Theorem

A statistical rule stating for any real number k greater than one, at least (1-1/k^2) of the distribution's values lie within k standard deviations from the mean.

Standard Deviations

A metric indicating the degree of spread or variability in a collection of numbers, highlighting the distance of individual values from the central mean.

Chebyshev's Theorem

A statistical theorem which states that for any real number greater than one, a certain proportion of values in any data set will be close to the mean, based on the number of standard deviations specified.

Standard Deviations

A measure of the amount of variation or dispersion of a set of values, indicating how spread out the values are from their mean.