Question

The bases of a 39-foot pole and a 15-foot pole are 45 feet apart, and both poles are perpendicular to the ground. The ground is flat between the two poles. What is the length of the shortest rope that can be used to connect the tops of the two poles?

Answer 1

Answer: 51 feet

Explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:

x^2 = a^2 + b^2

Where x is the hypotenuse of the triangle (in this case length of the rope) and a and b are the other sides.

The difference between the poles' heights is equal to one side of the triangle (39-15=24), the other side of the triangle is the distance between poles (45).

Replacing with the values given:

x^2 = 24^2 + 45^2

x^2 = 576+2,025

x^2 = 2,601

x = √2,601

x = 51 feet

Feel free to ask for more if needed or if you did not understand something.