Question

To support a young tree, Jack attaches a guy wire from the ground to the tree. The wire is attached to the tree 4 ft above the ground. If the angle formed between the wire and the tree is 70°, what is the length of the wire?

Answer 1

To find the length of the wire, we can use trigonometry to relate the angle and the height of the tree above the ground. Using the tangent function, we can solve for the length of the wire.

Step-by-step explanation:

To find the length of the wire, we can use trigonometry. We can use the tangent function to relate the angle and the length of the wire. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree above the ground and the adjacent side is the length of the wire. So we have:

tan(70°) = height of tree / length of wire

Plugging in the values we have, tan(70°) = 4 ft / length of wire. Rearranging the equation to solve for the length of the wire, we get:

length of wire = 4 ft / tan(70°)

Using a calculator, the length of the wire is approximately 12.69 feet.