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A boat is heading towards a lighthouse, where Serenity is watching from a vertical distance of 141 feet above the water. Serenity measures an angle of depression to the boat at point A to be
9°. At some later time, Serenity takes another measurement and finds the angle of depression to the boat ( now at point B ) to be 61°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.



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Respuesta :

okpalawalter8

A boat is heading towards a lighthouse, where Serenity is watching from a vertical distance of 141, the distance from point A to point B. is mathematically given as

BC=78.1575

What is the distance from point A to point B.?

Generally, the equation for the angle is mathematically given as

[tex]tan\theta=\frac{oop}{adj}[/tex]

Therefore

[tex]tan\theta=\frac{141}{AC}[/tex]

Therefore

[tex]AC=\frac{141}{tan 9}[/tex]

AC=890.2389

In conclusion, with triangle BDC

[tex]tan61=\frac{141}{BC}[/tex]

Therefore

BC=141/tan61

BC=78.1575

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