Question

solving problems with the pythagorean theorem
an airplane is flying directly over your house. the distance between your house and the airport is 12 miles. the altitude of the airplane is 4 miles. determine the distance between the airplane and the airport.
use the given scenario to answer each question.
use the variables in the diagram to complete the statement of the pythagorean theorem.
a² + =
the unknown side represents
substitute the given lengths into the pythagorean theorem to write an equation with one variable to determine the distance between the airplane and the airport. then solve for the unknown distance.

Explanation:

Step1: Identify sides for Pythagorean Theorem

Let $a = 4$ (altitude), $b=12$ (distance from house to airport), and $c$ be the distance from airplane to airport. Pythagorean Theorem is $a^{2}+b^{2}=c^{2}$. So the blanks are filled as $a^{2}+b^{2}=c^{2}$, where the first blank is $12^{2}$ and the second is $r^{2}$ (assuming $r$ is the distance from airplane to airport). The unknown side represents the distance between the airplane and the airport.

Step2: Substitute values into formula

Substitute $a = 4$ and $b = 12$ into $a^{2}+b^{2}=c^{2}$. We get $4^{2}+12^{2}=c^{2}$.

Step3: Calculate squares

$4^{2}=16$ and $12^{2}=144$. So the equation becomes $16 + 144=c^{2}$, i.e., $c^{2}=160$.

Step4: Solve for $c$

$c=\sqrt{160}=\sqrt{16\times10}=4\sqrt{10}\approx 12.65$ miles.

Answer:

The distance between the airplane and the airport is $4\sqrt{10}\approx12.65$ miles. The filled - in Pythagorean - Theorem statement is $a^{2}+12^{2}=r^{2}$, and the unknown side represents the distance between the airplane and the airport.