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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