Question

determine the altitude (height) of the plane in the image below. note: figure is not drawn to scale.

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the plane be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 610$ m and $b=110$ m, and $a = x$. So $x=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$x=\sqrt{610^{2}-110^{2}}=\sqrt{(610 + 110)(610 - 110)}$ (using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$). Then $x=\sqrt{(720)\times(500)}=\sqrt{360000}$.

Step3: Calculate the square - root

$x = 600$ m

Answer:

600 m