Answer:
the height of the antenna is 22 ft
Step-by-step explanation:
Hello
Step 1
the antenna, the cable and the ground form a right triangle,where
hypotenuse=cable =25 feet
adjacent side= ground = 12 feet
Opposite side=antenna=x
using the Pythagorean theorem
[tex]adjacent\ side^{2} +opposite\ side^{2} =hypotenuse^{2} \\[/tex]
put the values into the equation
[tex]adjacent\ side^{2} +opposite\ side^{2} =hypotenuse^{2} \\\\(12 ft)^{2} +x^{2}=(25ft)^{2} \\solve\ for\ x\\x^{2} =(25ft)^{2}-(12 ft)^{2}\\x=\sqrt{(25ft)^{2}-(12 ft)^{2}} \\x=\sqrt{625(ft)^{2}-144(ft)^{2} } \\x=\sqrt{481 (ft)^{2} }\\(it\ is\ a\ distance\ use\ just\ the\ positive\ root)\\x=21.93\ ft\\x=22\ ft\\[/tex]
the height of the antenna is 22 ft
have a good day.
