trig
posted by Dan on .
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?

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