The distance between water towers is 2.7 miles (rounded to the nearest tenth).
We know that we are dealing with a triangle. We have also been told two of the side lengths of the triangle (CA=1.2 miles and CB=1.8 miles). We have also been provided with one of the angles of the triangle (angle ACB=81 degrees). We are asked to find the length of the third side of the triangle (AB).
We can use the law of cosines to solve this problem. The law of cosines states that:
cos(A) = (b²+c²-a²)/(2bc)
where A is the angle between sides b and c, and A is the side opposite angle A.
In this problem, we are solving for side AB, so we can rewrite the law of cosines as follows:
AB = sqrt(b²+c²-2bc*cos(A))
where b=1.2 miles, c=1.8 miles, and A=81 degrees.
Plugging in the values, we get:
AB = sqrt(1.2²+1.8²-2*1.2*1.8*cos(81 degrees))
AB = 2.7 miles
Therefore, the distance between the water towers is 2.7 miles, to the nearest tenth of a mile.