Question

1. a 35 - foot wire is secured from the top of a flagpole to a stake in the ground. if the stake is 14 feet from the base of the flagpole, how tall is the flagpole?

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the flagpole be \(h\). The wire is the hypotenuse \(c = 35\) feet, and the base \(b=14\) feet. By the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), here \(a = h\), so \(h^{2}+14^{2}=35^{2}\).

Step2: Calculate \(h^{2}\)

\(h^{2}=35^{2}-14^{2}=(35 + 14)(35 - 14)\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)).
\(h^{2}=(49)(21)\)
\(h^{2}=1029\)

Step3: Find \(h\)

\(h=\sqrt{1029}=\sqrt{49\times21}=7\sqrt{21}\approx 32.1\)

Answer:

The height of the flagpole is approximately \(32.1\) feet.