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You are on a ship at sea. You see a lighthouse in the distance. You know the lighthouse is 175 feet tall. You measure the angle of elevation to the top of the lighthouse at 5 degrees. How far are you from the bottom of the lighthouse

Respuesta :

Answer: 2000.25 ft

Step-by-step explanation:

Given

Height of lighthouse [tex]h=175\ ft[/tex]

Angle of elevation [tex]\theta=5^{\circ}[/tex]

Suppose, you are x feet away from lighthouse

From the figure, we can write

[tex]\Rightarrow \tan 5^{\circ}=\dfrac{175}{x}\\\\\Rightarrow x=\dfrac{175}{\tan 5^{\circ}}\\\\\Rightarrow x=2000.26\ ft[/tex]

Thus, the ship is 2000.25 ft away from the light-house

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