trig

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?

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  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

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  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?

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