Question

Two radio towers have been positioned 8 miles apart at points a and b. point d is located exactly 4 miles from point a. the third tower will be placed at point c so that all three towers are equidistant from each other.

Answer 1

Let's call the distance from point C to point D as "x".

We know that the distance from A to B is 8 miles, and the distance from A to D is 4 miles. To ensure that all three towers are equidistant from each other, the distance from C to B must be equal to 8 miles.

Using the Pythagorean Theorem, we can find the distance from C to D:

`(x)^2 + (4)^2 = (8)^2`

Expanding and simplifying the equation:

`x^2 + 16 = 64`

`x^2 = 48`

`x = √(48) = 6.928`

So the distance from the third tower to point D is approximately 7 miles (rounded to the nearest tenth of a mile).