Question

Two towers are 30 feet apart. One is 20 feet high and the other is 10 feet high. There is a stake in the ground between the towers. The top of each tower has a wire tied to it that connects to the stake on the ground. Where should the stake be placed to use the least amount of wire?

Answer 1

The towers are 30 feets apart

The heights are given as : 20 feet and 10 feet high.

The stake is positioned between the towers.

Now use the idea of sine, cosine and tangents to find the length of the wire from both towers to the stake

Lets assume the stake is at the far end from the tower with 20 ft , so the distance from the stake to the tower will be 30 ft .Find the length of wire to be used by applying the pythagorean relationship where the leg distances will be 30ft and 20 ft.

so;

if a^2 + b^2 = c^2

30^2 + 20^2 = c^2

900 + 400 = c^2

1300 = c^2

36 ft

So with a height of 20 ft and maximum distance between each tower the length of the wire is 36 ft

For a height of 20 ft and maximum distance between each tower the length of wire is 18 ft

Now to get the point where the stake should be placed, have a sketch as shown below