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's height (22m) and Donna's horizontal distance from entrance (50m) form legs of a right triangle. The radio range is the hypotenuse.

Step2: Apply Pythagorean theorem

Let \( a = 22 \), \( b = 50 \), hypotenuse \( c \). Formula: \( c=\sqrt{a^{2}+b^{2}} \)
Substitute: \( c=\sqrt{22^{2}+50^{2}}=\sqrt{484 + 2500}=\sqrt{2984} \)

Step3: Calculate and round

\( \sqrt{2984}\approx54.63\approx55 \) (to nearest meter)

Answer:

B. 55 meters