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

## Answer This Question

## Related Questions

- Precalculus - 1. A man stands 12 feet from a statue. The angle of elevation from...
- maths - From the top of a cliff 150m high, the angles of depression of two boats...
- maths-urgently needed - From the top of a cliff 150m high, the angles of ...
- trig - A plane is flying 12,000 feet horizontally from a tall, vertical cliff. ...
- formal geomerty - A person in a small boat sights the top of a 40-foot ...
- math - A person in a lighthouse notices two boats out on the ocean. The angle ...
- Geometry - There is a flagpole in the school parking lot. Which of the ...
- Math - Two ships are sailing in the sea on the two sides of a lighthouse. The ...
- trigonometry - A lighthouse BC of unknown height stands on the edge of a cliff ...
- Math - From the top of a 50m high bridge, two boats are seen at anchor. One boat...

More Related Questions