Question

A pole 8 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Maya measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.

Answer 1

To find the length of the guy wire, we can use the Pythagorean theorem. The distance from the pole to the stake is one leg of the right triangle, and the distance from the pole to the tower is the other leg. The guy wire is the hypotenuse of the right triangle.

Let's label the distance from the pole to the stake as $a$ and the distance from the pole to the tower as $b$. We can see that $a = 6$ feet (the horizontal line segment in the diagram) and $b = 8$ feet (the height of the pole).

Now we can use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $c$ is the length of the guy wire.

Plugging in the values we found, we have $6^2 + 8^2 = c^2$.

Simplifying, $36 + 64 = c^2$.

Adding, $100 = c^2$.

Taking the square root of both sides, we find $c = \sqrt{100}$.

Simplifying, $c = 10$.

So the length of the guy wire is $\boxed{10}$ feet.