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

55 meters

Explanation:

A right triangle is formed, where one leg is the height of the building (let's call it x), the other leg is the distance between Donna and the entrance (let's call it y) and the hypotenuse is the distance between the two girls (let's call it z). From Pythagorean theorem:

z² = x² + y²

z = √(x² + y²)

Replacing with x = 22 m and y = 50 m we get the range of communication for the two radios.

z = √(22² + 50²)

z = 55 m

Answer 2

Using Pythagorean theorem: c^2 = a^2 + b^2, and if a = 22 and b = 50
c^2=484+2500
c=sqrt 2984
c=55 meters