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From the top of a lighthouse 280 feet tall, to keep her spot a ship in distress at an angle of depression of 18°. How far is the boat from shore(The base of the lighthouse) round to the nearest foot

Sagot :

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.

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