A pole has two guy wires attached to it. A 32.5-foot guy wire is attached 30 feet up the pole. A second guy wire is attached 15 feet further up the pole. The second guy wire is attached to the ground 8 feet further away from the pole than the first guy wire.

Question

A pole has two guy wires attached to it. A 32.5-foot guy wire is attached 30 feet up the pole. A second guy wire is attached 15 feet further up the pole. The second guy wire is attached to the ground 8 feet further away from the pole than the first guy wire.

part 1. To the nearest tenth of a foot, what is the distance, x, from the pole to the ground where the first guy wire is attached?
Part 2. To the nearest tenth of a foot, what is the length of the second guy wire? ( showed work)

Answer 1

Did you draw a diagram? If so, it should be clear that this is just an exercise in using the Pythagorean Theorem.

(1) x^2 + 30^2 = 32.5^2
(2) If the 2nd wire's length is z, then z^2 = (x+8)^2 + (30+15)^2

Answer 2

Part 1:

To find the distance from the pole to where the first guy wire is attached, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's denote the distance from the pole to the ground where the first guy wire is attached as x.

According to the problem, one side of the right triangle is 30 feet and the hypotenuse (the guy wire) is 32.5 feet.

Using the Pythagorean theorem, we have:

x^2 + 30^2 = 32.5^2

x^2 + 900 = 1056.25

x^2 = 156.25

x ≈ √156.25

x ≈ 12.5 feet

Therefore, to the nearest tenth of a foot, the distance from the pole to the ground where the first guy wire is attached is approximately 12.5 feet.

Part 2:

To find the length of the second guy wire, we can use the same approach.

According to the problem, the second guy wire is attached 15 feet further up the pole than the first guy wire. So the height from the ground to where the second guy wire is attached is 30 + 15 = 45 feet.

The second guy wire is attached to the ground 8 feet further away from the pole than the first guy wire. So the base of the triangle formed by the second guy wire is 30 + 8 = 38 feet.

Again, we can use the Pythagorean theorem to find the length of the second guy wire.

Let's denote the length of the second guy wire as y.

Using the Pythagorean theorem, we have:

y^2 + 38^2 = 45^2

y^2 + 1444 = 2025

y^2 = 581

y ≈ √581

y ≈ 24.1 feet

Therefore, to the nearest tenth of a foot, the length of the second guy wire is approximately 24.1 feet.