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 flag - pole be $h$, the distance from the base of the flag - pole to the stake be $a = 14$ feet and the length of the wire be $c=35$ feet. According to the Pythagorean theorem $a^{2}+h^{2}=c^{2}$, so $h^{2}=c^{2}-a^{2}$.

Step2: Substitute values

Substitute $a = 14$ and $c = 35$ into the formula: $h^{2}=35^{2}-14^{2}=(35 + 14)(35 - 14)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). Then $h^{2}=(49)(21)=1029$.

Step3: Calculate $h$

$h=\sqrt{1029}=\sqrt{49\times21}=7\sqrt{21}\approx 31.38$ feet.

Answer:

$7\sqrt{21}\approx31.38$ feet