Question

question
a pole 5 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, zoe 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.
(the diagram is not to scale.)
attempt 1 out of 2

Explanation:

Step1: Identify right - triangle

The situation forms a right - triangle with height 5 ft (height of the pole) and base 10 + 1=11 ft (distance from tower to stake via the pole).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(b = 11\), and \(c\) is the length of the guy - wire. So \(c=\sqrt{5^{2}+11^{2}}=\sqrt{25 + 121}=\sqrt{146}\).

Step3: Calculate and round

\(\sqrt{146}\approx12.083\). Rounding to the nearest foot, \(c\approx12\).

Answer:

12