Question

select the correct answer.
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 buildings 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

Explanation:

Step1: Use Pythagorean theorem

Let the distance from the entrance be \(x\). The height of the building \(h = 22\) meters. The maximum distance \(d\) (when the connection breaks) forms a right - triangle. By Pythagorean theorem \(d=\sqrt{x^{2}+h^{2}}\). Given \(x>50\), when \(x = 50\), \(d=\sqrt{50^{2}+22^{2}}=\sqrt{2500 + 484}=\sqrt{2984}\approx54.6\). As \(x\) increases, \(d\) increases.

Step2: Check the options

Since \(x>50\), when \(x\) is just greater than \(50\), \(d\) is just greater than \(\sqrt{50^{2}+22^{2}}\approx54.6\). Among the options \(55\) meters is the closest.

Answer:

B. 55 meters