Question

a flagpole casts a shadow on a flat concrete patio. the distance from the top of the pole to the tip of the shadow is 35 feet. the distance along the ground from the base of the pole to the tip of the shadow is 14 feet. what is the height of the flagpole? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply the Pythagorean theorem

Let the height of the flagpole be \(h\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 35\) (hypotenuse) and \(a=14\) (one - leg). We want to find \(b\) (the height of the flagpole), so \(h=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

Substitute \(c = 35\) and \(a = 14\) into the formula: \(h=\sqrt{35^{2}-14^{2}}=\sqrt{(35 + 14)(35 - 14)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)). Then \(h=\sqrt{49\times21}=\sqrt{1029}\).

Step3: Calculate the square root

\(\sqrt{1029}\approx32.1\)

Answer:

\(32.1\) feet