Question

A lighthouse that rises h1 = 48.3 ft above the surface of the water sits on a rocky cliff that extends d = 21.0 ft from its base, as shown in the figure below.

A sailor on the deck of a ship sights the top of the lighthouse at an angle of $$\theta$$ = 29.6$$\circ$$ above the horizontal. If the sailor's eye level is h₂ = 12.0 ft above the water, how far is the ship from the rocks?

Answer 1

Answer : 42.899 ft

you want to form a triangle to solve this.

one side will by 48.3 ft - 12ft = 36.3 ft
one side will be 21 ft + x , x is the distance of the ship from the rock

tan(29.6 degrees) = 36.3/(19+x)

tan(29.6) = 0.568

x = (36.3/0.568 ) - 21

= 63.89 - 21 = 42.899 ft

= 42.899 ft