Answer
1.91 miles
Work Step by Step
The lines between city hall, the church, and the first bridge make a triangle. As 2 angles are given as 25 degrees and 30 degrees, the other angle is 180 - 30 - 25 = 125 degrees.
As the 125 degree angle corresponds with the distance between city hall and the church, and the 30 degree angle corresponds with a known length, we can use the law of sines ($\frac{sin(A)}{A}$ = $\frac{sin(B)}{B}$ = $\frac{sin(C)}{C}$) to get this:
$\frac{sin(125)}{x}$ = $\frac{sin(30)}{0.86miles}$, where x is the distance between city hall and the church. This simplifies to $\frac{sin(125)}{x}$ = $\frac{0.5}{0.86miles}$, or x = $\frac{sin(125)}{0.43}$ $\approx$ 1.91 miles.
