From a boat on the river below a dam, the angle of elevation to the top of the dam is 15 degrees 35'. if the dam is 2083 feet above the level of the river how far is the boat from the base of the dam to the nearest foot

Answer 1

how about
tan 15°35' = 2083/x, where x is the horizontal distance you want
x = 2083/tan
= 2083/.278891.... = 7468.85 ft or 7469 ft to the nearest foot

check:
tan^-1 (2083/7468.85) = 15.58333...°
= 15° .58333...*60'
= 15° 35'

Answer 2

tan 15 35/60 deg = 2083 / d
so
d = 2083 / 0.27889