Question

Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a building that is 22 meters high with one of the radios and stands directly above the building’s entrance. Donna walks out of the entrance, perpendicular to the building, with the other radio. If Donna is more than 50 meters from the entrance, the connection between the radios breaks. What is the range of communication for the two radios to the nearest meter? A) 50 meters B) 55 meters C) 62 meters D) 72 meters

Answer 1

This question is far easier to understand if we draw it out. I've included an image attachment to help show the relationships of the measurements. As we can see from the image, their positioning helps form a triangle that we can use the Pythagorean Theorem to find the connection range.
The Theorem is $a^2 + b^2 = c^2$ where a and b are the legs and c is the hypotenuse.

$22^2 + 50^2 = c^2$
$484 + 2500 = c^2$
$2984= c^2$
$\sqrt{2984} = c$
$54.63 = c$
So the answer to the nearest meter is 55 meters.