



 
Hi Scott, I drew a diagram of what I think you are describing and added some line segments. $C$ is the center of the circle and $M$ is the midpoint of $AB.$ By the symmetry of the figure the measure of the angle $BCA$ is $\large \frac{360}{5} \normalsize = 72$ degrees. Again using the symmetry the angle $CMB$ is a right angle and the measure of the angle $BCM$ is $\large \frac{72}{2} \normalsize = 36$ degrees. Also $CB$ is a radius of the circle so its length, $BC$ is 7.5 feet. \[\sin \left(BCM \right) = \sin(36^o ) = \frac{MB}{BC} \] Hence you can calculate the length of $MB.$ The cord $AB$ subtends the angle $BCA$ at the center of the circle and the angle $BPA$ at the circumference of the circle and hence the measure of the angle $BPA$ is half the measure of the angle $BCA.$ Thus the measure of the angle $BPM$ is $18^{o}.$ Can you now use the right triangle $BPM$ to calculate the length of $BP?$ write back if you need more assistance, 



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