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

Answer 1

Draw altitude CD, length x (we want).
let y = AD
then 125 - y = BD
tan 65 40 = x/ (125-y)
tan 54 30 = x/y
solve for x and y, you need x, the altitude.

Answer 2

If the width is w, then
wcotA + wcotB = 125
w = 125/(cot65°40' + cot54°30')