Question

a wire extends from the top of a 72 foot flag pole to a stake in the ground 21 feet away. how long is the wire?

Explanation:

Step1: Identify right - triangle

The flag - pole, the ground, and the wire form a right - triangle. The height of the flag - pole is one leg ($a = 72$ feet) and the distance from the base of the flag - pole to the stake is the other leg ($b = 21$ feet). The wire is the hypotenuse ($c$).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. Substitute $a = 72$ and $b = 21$ into the formula: $c^{2}=72^{2}+21^{2}$.
$c^{2}=5184 + 441$.
$c^{2}=5625$.

Step3: Solve for $c$

Take the square root of both sides: $c=\sqrt{5625}=75$.

Answer:

75 feet