an electrician needs to run a cable from the top of a 48-foot tower to a transmitter box located 20 feet away from the base of the tower. Find how long he should cut the cable.
52
Draw a diagram, and you can see that the desired length x is
x^2 = 48^2 + 20^2
An electrician needs to run a cable from the top of a 48-foot tower to a transmitter box located 20feet away from the base of the tower. Find how long he should make the cable.
52
Why did the electrician bring a tape measure to the tower?
Because he wanted to make sure he didn't come up short!
Now, let's calculate the length of the cable. Let's use the Pythagorean theorem: a² + b² = c².
The height of the tower is 48 feet and the distance from the base to the transmitter box is 20 feet.
So, the equation becomes 48² + 20² = c².
Which gives us: 2,304 + 400 = c².
Adding up those numbers, we get 2,704 = c².
Now, we'll take the square root of both sides to find the length of the cable.
√2,704 = √c².
That gives us c = √2,704.
The square root of 2,704 is approximately 52 feet.
So, the electrician should cut the cable to be around 52 feet long. However, it's always wise to add a few extra feet just to be safe.
To find the length of the cable that the electrician needs to cut, we can use the Pythagorean theorem. The theorem states that in a right-angled 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 tower forms the vertical side, the distance from the base of the tower to the transmitter box forms the horizontal side, and the cable is the hypotenuse.
Let's label the length we need to find as 'c' (the length of the cable), the height of the tower as 'a', and the horizontal distance from the base of the tower to the transmitter box as 'b'.
Using the Pythagorean theorem, we have the equation:
c^2 = a^2 + b^2
To solve for 'c', we can substitute the given values:
a = 48 feet (height of the tower)
b = 20 feet (horizontal distance from base to transmitter box)
Plugging in these values, we get:
c^2 = 48^2 + 20^2
Performing the calculation:
c^2 = 2304 + 400
c^2 = 2704
To find the value of 'c', we take the square root of both sides:
c = √2704
c ≈ 52 feet
Therefore, the electrician should cut the cable to a length of approximately 52 feet.