Question

A 25 foot cable is stretched from the top of an antenna to an anchor point on the ground. How tall is the antenna if the anchor point is 12 feet from the base of the antenna (rounded to the nearest foot)?

A) 20 ft
B) 21 ft
C) 22 ft
D) 23 ft

Answer 1

this is the same as finding the sides of a triangle.
12^2 + X^2 = 25^2
144 + X^2 = 625
625 - 144 = 481
481 squared = 21.9317
round that up and you get 22. Hope that helps!

Answer 2

the height of the antenna is 22 ft

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

`adjacent\ side^(2) +opposite\ side^(2) =hypotenuse^(2) \\`

put the values into the equation

`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\\`

the height of the antenna is 22 ft

have a good day.