Question

a telephone pole is 8 meters tall and a pigeon is standing on the ground 2 meters from the pole. if the pigeon flies from where it is standing to the top of the telephone pole, how far will it fly? if necessary, round to the nearest tenth. meters

Explanation:

Step1: Identify the right - triangle

The telephone pole, the ground from the base of the pole to the pigeon, and the path of the pigeon's flight form a right - triangle. The height of the pole \(a = 8\) meters and the base \(b=2\) meters. We use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).

Step2: Substitute values into the Pythagorean theorem

Substitute \(a = 8\) and \(b = 2\) into the formula \(c=\sqrt{8^{2}+2^{2}}\). First, calculate \(8^{2}=64\) and \(2^{2} = 4\). Then \(a^{2}+b^{2}=64 + 4=68\). So \(c=\sqrt{68}\).

Step3: Simplify the square root

We know that \(\sqrt{68}=\sqrt{4\times17}\). Since \(\sqrt{4\times17}=\sqrt{4}\times\sqrt{17}\) and \(\sqrt{4} = 2\), then \(c = 2\sqrt{17}\approx2\times4.123\approx8.2\).

Answer:

\(8.2\)