Posted by **Dan** on Saturday, October 1, 2011 at 11:19am.

The captain of a ship at sea sights a lighthouse which is 120 feet tall.

The captain measures the the angle of elevation to the top of the lighthouse to be 19 ^\circ.

How far is the ship from the base of the lighthouse?

- trig -
**Anonymous**, Saturday, October 1, 2011 at 12:53pm
H = Hight of lighthouse

L = Distance between a ship and a lighthouse

tan( theta ) = H / L

If 19^ mean 19° then:

tan( theta ) = H / L

tan( 19° ) = 120 / L

L * tan( 19° ) = 120 Divide both sides with tan( 19° )

L = 120 / tan ( 19° )

L = 120 / 0.34433

L = 348.5 ft

If 19^ mean 19´ then:

tan( theta ) = H / L

tan( 19´ ) = 120 / L

L * tan( 19´ ) = 120 Divide both sides with tan( 19´ )

L = 120 / tan ( 19´ )

L = 120 / 0.00553

L = 21,699.82 ft

If 19^ mean 19" then:

tan( theta ) = H / L

tan( 19" ) = 120 / L

L * tan( 19" ) = 120 Divide both sides with tan( 19" )

L = 120 / tan ( 19" )

L = 120 / 0.00009

L = 1,333,333.33 ft

## Answer This Question

## Related Questions

- trig - The captain of a ship at sea sights a lighthouse which is 280 feet tall. ...
- Calculus - The captain of a ship at sea sights a lighthouse which is 260 feet ...
- Maths - An observer at the top of a lighthouse 55m Hugh sights a ship at a sea ...
- Maths - A ship is sighted from the top of a lighthouse. The angle of depression ...
- trigonometry - From a ship, the angle of elevation of the top of the lighthouse ...
- math - the angle of elevation from a ship to a 135-foot-tall lighthouse is 2 ...
- Math, trigonometry - An observer in a lighthouse 47m high sights a ship at at ...
- Geometry - how do I set up this problem a man standing on the deck of a ship ...
- Geometry - how do I set up this problem a man standing on the deck of a ship ...
- GEOMETRY - cASEY SIGHTS THE TOP OF AN 84 FOOT TALL LIGHTHOUSE AT AN ANGLE OF ...

More Related Questions