A power line is attached at the same height to two utility poles that are separated by a distance of 100 ft; the power line follows the curve f(x) = a cosh(x/a). Use the following steps to find the value of a that produces a sag of 10 ft midway between the poles. Use a coordinate system that places the poles at x = ±50. 

a. Show that a satisfies the equation cosh(50/a) - 1 = 10/a.

b. Let t = 10/a, confirm that the equation in part (a) reduces to cosh 5t - 1 = t, and solve for t using a graphing utility. Report your answer accurate to two decimal places.

c. Use your answer in part (b) to find a and then compute the length of the power line.