Posted by Romar on Saturday, July 20, 2013 at 2:24am.
A lighthouse standing on the top of a cliff is observed from two open boats (boats are not decked over) A and B in a vertical plane through the light house. The angle of elevation of the top of the lighthouse viewed from B is 16 degrees and the angles of elevation of the top and bottom viewed from A are 40 degrees and 23 degrees respectively. If the boats are 1320 ft. apart, find the height of the lighthouse and the height of the cliff.

physics  Steve, Saturday, July 20, 2013 at 3:20pm
c = cliff height
h = lighthouse hight
a = distance of A from cliff
b = distance of B from cliff
c/a = tan 23°
(c+h)/a = tan 40°
(c+h)/b = tan 17°
So, clearing fractions and plugging in the trig values, we have
c = .4245a
c+h = .8391a
c+h = .3057b
b = a+1320
h = 313.65
c = 321.14
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