Question

30 ft cable extends from the floor of the lookout of a fire tower. The cable is anchored to the ground 18 ft away from the base of the tower. What is the height of the floor of the lookout tower?

Answer 1

The height would be 24 ft

Answer 2

The height of the tower is 24 ft.

Explanation:

Consider the provided information,

The cable length is given as 30ft.

The distance of cable anchored to the ground is 18ft.

And we need to find the height of the tower.

We can find this with the help of Pythagorean theorem.

`a^2+b^2=c^2`

Where a and b are the legs and c is the hypotenuse.

Now substitute a=18 and c=30 and solve for b as shown.

`(18)^2+b^2=(30)^2`

`324+b^2=900`

`b^2=900-324`

`b^2=576`

`b=√(576)`

`b=24`

Hence, the height of the tower is 24 ft.