Question

a pole 9 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, ella 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. (diagram is not to scale.)

Explanation:

Step1: Identify similar triangles

The pole and tower form two right triangles that are similar, so their side ratios are equal. Let $h$ = height of tower segment from ground to guy wire attachment.
$\frac{h}{10+1} = \frac{9}{1}$

Step2: Solve for tower height

Calculate the height of the tower at the guy wire:
$h = 9 \times 11 = 99$ feet

Step3: Apply Pythagorean theorem

Use the right triangle with legs $h=99$ ft and total ground distance $11$ ft to find guy wire length $L$:
$L = \sqrt{99^2 + 11^2}$

Step4: Compute the value

Calculate the squares and sum:
$99^2 = 9801$, $11^2 = 121$, $9801+121=9922$
$L = \sqrt{9922} \approx 99.61$

Step5: Round to nearest foot

Round the result to the closest whole number:
$\approx 100$

Answer:

100 feet