A wire is stretched from the ground to the top of an antenna tower. The wire is 20 feet long. The height of the tower is 4 feet greater than the distance from the tower's base to the end of the wire. Find the height of the tower.
20 ft.= w
x.4 = height of tower
something like this?
Well, this is a tall order, but I'll give it a shot! Let's break it down, shall we?
So, we have a wire that is 20 feet long, and it's stretched from the ground to the top of the tower. We want to find the height of the tower, right?
Now, here's the fun part! The height of the tower is actually 4 feet greater than the distance from the tower's base to the end of the wire. Hmmm, tricky!
Let's call the distance from the tower's base to the end of the wire "x". So, according to the information we have, the height of the tower can be expressed as x + 4.
But hold your horses! We also know that the wire is 20 feet long, and it's stretched from the ground to the top of the tower. So, we can create an equation: x + (x + 4) = 20.
Now, let's do a little math magic. Simplifying the equation, we have 2x + 4 = 20. Let's wave our wand and get rid of the 4 by subtracting it from both sides. Voila! We're left with 2x = 16.
One final spell to solve for x! We'll divide both sides by 2, and abracadabra, x = 8. So, the distance from the tower's base to the end of the wire is 8 feet.
Now, remember that the height of the tower is x + 4, so 8 + 4 = 12. Ta-da! The height of the tower is 12 feet.
I hope I didn't twist your brain too much with my circus of calculations!
Yes, you're on the right track! Let's define some variables to help us solve the problem.
Let's say the height of the tower is h feet, and the distance from the tower's base to the end of the wire is d feet.
According to the problem statement, the wire is 20 feet long, so we have the equation:
w + d = 20
The height of the tower is given as 4 feet greater than the distance from the tower's base to the end of the wire, so we can write:
h = d + 4
Now we have a system of two equations with two variables. To solve it, we can substitute the second equation into the first equation:
w + (h - 4) = 20
Now let's substitute the value of w from the given information, which is w = 20:
20 + (h - 4) = 20
Simplifying this equation, we get:
h - 4 = 0
Solving for h, we add 4 to both sides:
h = 4
Therefore, the height of the tower is 4 feet.
To solve this problem, we can set up a simple equation based on the given information.
Let's denote the height of the tower as 'h' and the distance from the tower's base to the end of the wire as 'd.'
From the problem statement, we know that the wire is 20 feet long. Therefore, we can express this relationship as:
w = d + h
We are also given that the height of the tower is 4 feet greater than the distance from the tower's base to the end of the wire. This can be written as:
h = d + 4
Now we have two equations:
w = d + h
h = d + 4
We can substitute the value of 'h' from the second equation into the first equation to solve for 'd':
w = d + (d + 4)
20 = 2d + 4
16 = 2d
d = 8
Now that we have found the value of 'd,' we can substitute it back into the second equation to find the height of the tower:
h = d + 4
h = 8 + 4
h = 12
Therefore, the height of the tower is 12 feet.
I must assume that the wire's base is attached at some distance from the bottom of the tower, like a "guy-wire".
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Let the tower's height be H and the length of the wire be L = 20.
Use the Pythagorean theorem:
20^2 = H^2 + (H-4)^2
and solve for H.
400 = 2 H^2 -8H + 16
H^2 -4H -192
(H-16)(H+12) = 0
Take the positive root, H = 16 feet.
The tower's base is sqrt (20^2 - 16^2) = 12 feet from where the cable touches the ground.