Question

a pole 6 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, ian 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 right - triangle

The situation forms a right - triangle where the height of the pole is one leg ($a = 6$ ft), and the total horizontal distance from the base of the tower to the stake is the other leg ($b=15 + 4=19$ ft), and the guy - wire is the hypotenuse $c$.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 6$ and $b = 19$ into the formula: $c=\sqrt{6^{2}+19^{2}}=\sqrt{36 + 361}=\sqrt{397}$.

Step3: Calculate the value

$\sqrt{397}\approx19.92$. Rounding to the nearest foot, $c\approx20$ ft.

Answer:

20 ft