The captain of a boat knows that a lighthouse on the coast is 100 ftaway. If she measures the angle from the boat looking up to the topof the light house to be 2º and she is 4 feet above the water when shetakes this measurement, how tall is the light house?

Accepted Solution

Answer:Height of the light house [tex]=7.5\ feet[/tex]Step-by-step explanation:Distance of light house from boat = 100 ftAngle of elevation from boat to the top of light house = 2°Height above water while taking measurement = 4 ftThe figure of the situation is shown below.For Δ ABC[tex]\tan2\°=\frac {AB}{BC}[/tex][tex]\tan2\°=\frac {AB}{100}[/tex][tex]0.035=\frac {AB}{100}[/tex]Multiplying both sides by 100.[tex]100\times 0.035=100\times\frac {AB}{100}[/tex][tex]3.5=AB[/tex]∴ [tex]AB=3.5[/tex]Height of the light house [tex]=3.5+4=7.5\ feet[/tex]