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

Question

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?

Answer 1

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 2

The captain of a ship at sea sights a lighthouse which is 160 feet tall. The captain measures the the angle of elevation to the top of the lighthouse to be 17 °. How far is the ship from the base of the lighthouse?