Three highways connect the centers of three towns and
form a triangle. A cell phone company wants to place a
new cell tower so that it is the same distance from the
centers of the three towns. How can the company find
where to place the tower? Explain.

we know that

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. It is also the center of the circumcircle, the circle that passes through all three vertices of the triangle

The distance of the circumcenter to the vertices of the triangle is equal to the radius of the circle

see the attached figure to better understand the problem

therefore

the answer is

The cell phone company must be place the new cell tower in the circumcenter of the triangle formed by the center of the three towns

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

the answer is 18 units because there are 18 small cubes inside the rectangle

hope this and p.s i am also in k12

step-by-step explanation: