A wire is stretched from the ground to the top of an antenna tower. The wire is 30 feet long. The height of the tower is 6 feet greater than the distance d from the towers base to the end of the wire. Find the distance d and the height of the tower

The distance d is 18 feet.

The height of the tower is 24 feet.

Explanation:

The length of the wire is 30 feet.

The height of the tower is

where d is the distance of the towers base to the end of the wire.

Using Pythagorean theorem, we have,

Simplifying, we have,

Using quadratic formula, we shall determine the value of d.

Thus, we have,

 and  

Since, the value of d cannot be negative.

Thus,

Hence, the distance from the tower's base to the end of the wire is 18 feet.

Substituting in , we get,

Thus, the height of the tower is 24 feet.

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