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

select the correct answer.\nlyra 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?\n\na. 50 meters\nb. 55 meters\nc. 62 meters\nd. 72 meters

select the correct answer.\nlyra 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?\n\na. 50 meters\nb. 55 meters\nc. 62 meters\nd. 72 meters

Answer

Explanation:

Step1: Identify the right - triangle

The height of the building forms one leg ($a = 22$ meters) of a right - triangle, the distance Donna walks from the entrance forms the other leg ($b$), and the range of the radio is the hypotenuse ($c$). When the connection breaks, $b = 50$ meters.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 22$ and $b = 50$ into the formula: $c=\sqrt{22^{2}+50^{2}}=\sqrt{484 + 2500}=\sqrt{2984}$.

Step3: Calculate the value of $c$

$\sqrt{2984}\approx54.6$. Rounding to the nearest meter, $c\approx55$ meters.

Answer:

B. 55 meters