select the correct answer. lyra and donna are testing the two - way radios they built for their high school…

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?\na. 50 meters\nb. 55 meters\nc. 62 meters\nd. 72 meters

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?\na. 50 meters\nb. 55 meters\nc. 62 meters\nd. 72 meters

Answer

Explanation:

Step1: Identify the right - triangle

The situation forms a right - triangle. The height of the building is one leg ($a = 22$ meters) and the distance Donna walks is the other leg ($b>50$ meters). The range of communication is the hypotenuse $c$ of the right - triangle. According to the Pythagorean theorem, $c=\sqrt{a^{2}+b^{2}}$, where $a = 22$ and $b>50$.

Step2: Calculate the minimum value of $c$

When $b = 50$, $c=\sqrt{22^{2}+50^{2}}=\sqrt{484 + 2500}=\sqrt{2984}\approx54.6$. Since $b>50$, $c>54.6$.

Step3: Check the options

The smallest value among the options that is greater than $54.6$ is $55$ meters.

Answer:

B. 55 meters