Question

a cell tower is located 2 miles east and 5 miles north of a small town. the cell tower has a coverage radius of 4 miles. A house is located 7 miles north of the center of the town and is to the east of the cell tower. if the house lies on the boundary of the cell towers coverage, how far east of thr center of the town is the house?

Answer 1

The attached figure represents the explanation of the problem.

The distance between the house and the point B = 7 - 5 = 2

The distance between the house and the cell tower = 4

While the angle B is a right angle.

So, The distance between the house and the cell tower represents the hypotenuse

x and the distance between the house and the cell tower will be the legs

So, x = $\sqrt{4^2 - 2^2} = \sqrt{16 - 4} =\sqrt{12} =3.464$

The east distance between Town and House = 2 + x = 2 + 3.464 = 5.464 ≈ 5.5 miles

So, The house will be located 5.5 miles east of the town