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MAVERICK [17]
2 years ago
14

A wire is stretched from the ground to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3 feet

greater than the distance d from the tower's base to the end of the wire. Find the distance d and the height of the tower.
Mathematics
1 answer:
Mariana [72]2 years ago
8 0

The distance d is 9 ft and the height is 12ft.

<h3>How to find the distance and the height?</h3>

Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.

The height is one cathetus and the distance is the other catheti.

Let's define:

  • h = height
  • d = distance.
  • hypotenuse = 15ft

We know that the height of the tower is 3 ft larger than the distance, then:

h = d + 3ft

Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.

Then:

d^2 + (d + 3ft)^2 = (15ft)^2

Now we can solve this equation for d:

d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0

Then the solutions are:

d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}

We only take the positive solution:

d = (-3ft + 21ft)/2 = 9ft

And the height is 3 ft more than that, so:

h = 9ft + 3ft = 12ft

The distance d is 9 ft and the height is 12ft.

If you want to learn more about right triangles:

brainly.com/question/2217700

#SPJ1

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