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 31 feet. the distance along the ground from the base of the pole to the tip of the shadow is 25 feet. what is the height of the flagpole? provide an answer accurate to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the flag - pole be $h$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 31$ (hypotenuse) and $a = 25$ (one leg), and $b=h$. So $h^{2}+25^{2}=31^{2}$.

Step2: Rearrange the formula to solve for $h$

$h^{2}=31^{2}-25^{2}$. Then $h^{2}=(31 + 25)(31 - 25)$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). So $h^{2}=(56)\times(6)=336$.

Step3: Calculate the value of $h$

$h=\sqrt{336}\approx18.3$.

Answer:

$18.3$ feet