Answer: radius = 108.75 feet
Hi!
In the drawing you can see the arch that goes from point A to B. The right line from A to B is the length L = 150 feet, across the river. The height is h = 30 feet.
There is a right triangle with hypotenuse R, and the legs are (R-h), and L/2. The Pythagorean theorem says that:

Then:

Plugging the values of L and h, you get R = 108.75 feet