Question

A line AB, 125 feet long, is measured along the sraight bank of a river. A point C is on the opposite bank. Angles ABC and BAC are found to be 65° 40' and 54° 30' respectively. How wide is the river?

Answer 1

If you drop an altitude from C to AB, call it P, and if AP=x then BP = 125-x. Then the river's width is CP. Call that w. We then have

w cotA + w cotB = 125
w = 125/(cotA+cotB)

Now just plug in your values for A and B.