Can someone show how to solve this problem

Question

Two vertical towers of heights 60 ft and 80 ft stand on level ground, with their bases 100 ft apart. A cable that is stretched from the top of one pole to some point on the ground between the poles, and then to the top of the other pole. What is the minimum possible length of cable required? Justify your answer completely using calculus

Thanks!

Answer 1

If the point on the ground is x ft from the 60' tower, then the cable needed is

z = √(x^2+60^2) + √((100-x)^2 + 80^2)

minimum z is where dz/dx = 0

Answer 2

1850