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?

Answer 1

They will be forming a right triangle.

long leg is the height of Lyra. 22 meters high from the entrance.
short leg is the distance of Donna. 50 meters from the entrance.
We need to solve for the hypotenuse or the range of communication.

a² + b² = c²
22² + 50² = c²
484 + 2500 = c²
2,984 = c²
√2,984 = √c²
54.63 = c

The range of communication for the two radios is 55 meters.