Question

The captain of a boat knows that a lighthouse on the coast is 100 ft

away. If she measures the angle from the boat looking up to the top
of the light house to be 2º and she is 4 feet above the water when she
takes this measurement, how tall is the light house?

Answer 1

Height of the light house
`=7.5\ feet`

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

`\tan2\°=\frac {AB}{BC}`

`\tan2\°=\frac {AB}{100}`

`0.035=\frac {AB}{100}`

Multiplying both sides by 100.

`100* 0.035=100*\frac {AB}{100}`

`3.5=AB`

∴
`AB=3.5`

Height of the light house
`=3.5+4=7.5\ feet`