Answer:
Height of the light house [tex]=7.5\ feet[/tex]
Step-by-step explanation:
Distance of light house from boat = 100 ft
Angle of elevation from boat to the top of light house = 2°
Height above water while taking measurement = 4 ft
The 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]
