A wire is stretched from the ground to the top of an antenna tower. The wire is 17 feet long. The height of the tower is 7 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

Therefore,

The distance d is 8 feet,

and the height of the tower is 15 feet.

Step-by-step explanation:

Consider a diagram shown below such that

Let,

AC = length of wire = 17 feet

BC = d = distance from the tower's base to the end of the wire.

The height of the tower is 7 feet greater than the distance d

AB = height of tower = 7 +d

To Find:

AB = ? ( height of tower)

BC = d =?

Solution:

In Right Angle Triangle ABC by Pythagoras theorem we have

Substituting the values we get

Using (A+B)²=A²+2AB+B² we get

Dividing through out by 2 we get

Which is a quadratic equation, so on factorizing we get

d cannot be negative therefore ,

Now substitute d in AB we get

Therefore,

The distance d is 8 feet,

and the height of the tower is 15 feet.

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