help me start this?

Question

Two vertical poles of lengths 6 ft and 8 ft stand on level ground, with their bases 10 ft apart. Approximate the
minimal length of cable that can reach from the top of one pole to some point on the ground between the poles
and then to the top of the other pole.

Answer 1

Draw a diagram. Let x denote the distance along the ground from the base of the 6 ft. pole to where the cable touches the ground; then (10-x) is the distance along the ground from this point to the base of the 8 ft. pole. The length of the cable from the top of the 6 ft. pole to the ground is √(36 + x²) and the length of the cable from the top of the 8 ft. pole is √[64 + (10-x)²]

For minimizing, you should get x = 30/7, which results in a cable length of about 17.205 ft. (Technically, you should also check the endpoints x=0 and x=10.)

Hint: in the course of solving this, don't multiply out the (10-x)² term.

Answer 2

i come up with about 17.25. If the cable hits the ground at the half way point between the poles(5 ft), you have 2 right triangles. Using the Pythagorean Theorem, figure out the 2 hypotenuses and add them to get your answer. SQR of 25 + 36 and SQR of 25 and 64 , or SQR 61 and SQR89 , or 7.81 + 9.43 or 17.24 or so.