An electrician needs to run a cable from the top of a 40-foot tower to a transmitter box located 30feet away from the base of the tower. Find how long he should make the cable
I bet it is a 3-4-5 triangle.
However, in real life, such a cable would be foolish as an antenna feed, due to wind load, and worse, lighting which strikes the tower...the impedance of the tower would be far greater to lightening current flow than the cable, and as a result, the transmaitter box would be toast.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the height of the tower forms one side of the right triangle, and the distance from the base of the tower to the transmitter box forms the other side. The cable will act as the hypotenuse.
So, we need to find the length of the cable (the hypotenuse).
Let's call the length of the cable "c", the height of the tower "a", and the distance from the base of the tower to the transmitter box "b".
According to the Pythagorean theorem, we have:
c^2 = a^2 + b^2
Substituting the given values:
c^2 = 40^2 + 30^2
c^2 = 1600 + 900
c^2 = 2500
Taking the square root of both sides:
c = √2500
c = 50
Therefore, the electrician should make the cable 50 feet long.