You are planning a radio tower installation.

Question

you are planning a radio tower installation. The tower will be 100 feet tall, and it must be supported by four guy-wires that make an angle of at least 20 degrees at the top of the tower. how far from the base of the tower should be bottom of the guy=-wires be anchored? And how much wire should you order from your supplier? (Remember there are four-wires)

Answer 1

Draw and label a diagram

d represents the distance from the bas of the tower to the anchor

w represents the length of the wire

sin 70° = 100 /.w

tan 70° = 100 / d

Can you solve for w and d and answer

Answer 2

It's all about a right triangle. The 100-foot tower is one side; the distance of the anchoring spot (on the ground) from the bottom of the tower is the other side; the length of one wire from the top of the tower to the anchoring spot is the hypoteneus. The key is the 20-degree angle the wire makes from the tower top. The tangent of this angle is the side opposite (or d for the anchoring spot distance) over the side adjacent (100).

tan 20 = d/100

100(tan 20) = d

100(0.364) = d

36.4 = d

We can use the Pythagorean Theorem to find the hypoteneus (or wire length).

100^2 + 36.4^2 = w^2

One wire's length is the square root of 10,000 plus 1,324.96.

Four wires = 4(that length) rounded upward to the next foot.