Question

an observer on a cliff 1200 feet above sea level sights two ships due East. The angle of depression to the shops are 48° and 33°. What is the distance between the ships?

Answer 1

See the attached figure to better understand the problem

we know that
in the triangle ABC
tan 48°=AB/AC--------> AC=AB/tan48°------> 1200/tan 48°------> 1080.48 ft

in the triangle ABD
tan 33°=AB/AD---------> AD=AB/tan 33°-----> 1200/tan 33°------> 1847.88 ft

the distance between the ships is AD-AC---> 1847.88-1080.48----> 767.4 ft

the answer is 
the distance between the ships is 767.4 ft