Question

a flagpole casts a shadow on a flat concrete patio. the pole is 8 feet tall. the distance from the top of the pole to the tip of the shadow is 44 feet. what is the distance along the ground from the base of the pole to the tip of the shadow? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the distance along the ground be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 44\) (hypotenuse), \(a=x\), \(b = 8\). So \(x^{2}+8^{2}=44^{2}\).

Step2: Solve for \(x\)

First, calculate \(8^{2}=64\) and \(44^{2}=1936\). Then \(x^{2}=1936 - 64\).
\(x^{2}=1872\). Take the square root of both sides: \(x=\sqrt{1872}\).
\(\sqrt{1872}\approx43.3\)

Answer:

\(43.3\) feet