Question

a guy wire is a wire used to support telephone poles. suppose that a guy wire is located 15 feet up a telephone pole and is anchored to the ground 5 feet from the base of the pole. how long is the guy wire?

the guy wire is feet long.
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

🆕 New Concept Discovered: Pythagorean Theorem
Using right triangles to find missing sides

Step 1: Identify the right triangle

The telephone pole stands perpendicular to the ground, forming a right angle.

• The height up the pole is one leg: \( a = 15 \) feet.
• The distance along the ground from the base of the pole to the anchor is the other leg: \( b = 5 \) feet.
• The guy wire represents the hypotenuse: \( c \).

Step 2: Apply the Pythagorean theorem

The Pythagorean theorem states that in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:

$$ a^2 + b^2 = c^2 $$

Substitute the known values into the formula:

$$ 15^2 + 5^2 = c^2 $$

$$ 225 + 25 = c^2 $$

$$ 250 = c^2 $$

Step 3: Solve for the hypotenuse

Take the square root of both sides to find the length of the guy wire \( c \):

$$ c = \sqrt{250} $$

Simplify the radical:

$$ c = \sqrt{25 \times 10} = 5\sqrt{10} $$

Calculate the decimal value and round to three decimal places:

$$ c \approx 15.811388... $$

$$ c \approx 15.811 \text{ feet} $$

Answer:

15.811