Given:
Height of the lighthouse = 280 feet
The angle of depression from the top of the lighthouse to a ship = 18°.
To find:
The distance between boat and shore.
Solution:
Draw a diagram by using the given information.
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In triangle ABC,
[tex]\tan C=\dfrac{AB}{BC}[/tex]
[tex]\tan 18^\circ=\dfrac{280}{BC}[/tex]
[tex]BC=\dfrac{280}{\tan 18^\circ}[/tex]
Using a calculator, we get
[tex]BC=\dfrac{280}{0.3249}[/tex]
[tex]BC=861.80363...[/tex]
[tex]BC\approx 862[/tex]
Therefore, the boat is 862 feet away from shore.
