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 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

Explanation:

Step1: Identify the right triangle

Lyra is 22 meters high (vertical leg), Donna is 50 meters from the entrance (horizontal leg). The radio range is the hypotenuse.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \( c = \sqrt{a^2 + b^2} \), where \( a = 22 \), \( b = 50 \).
Calculate \( a^2 = 22^2 = 484 \), \( b^2 = 50^2 = 2500 \).
Sum: \( 484 + 2500 = 2984 \).
Take square root: \( \sqrt{2984} \approx 54.62 \), nearest to 55.

Answer:

B. 55 meters