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matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on a lake is 42 degrees. how far is the boat from matt

Respuesta :

Answer:

So, the distance from boat to matt is 455.81535feet

Step-by-step explanation:

We are given height of a cliff is 305 feet

and the measurement of the angle of depression to a boat on a lake is 42 degrees

so, we can draw diagram

Let's assume

distance from boat to matt is x

We can use trig

[tex]sin(42)=\frac{305}{x}[/tex]

now, we can solve for x

[tex]x=\frac{305}{sin(42)}[/tex]

[tex]x=455.81535feet[/tex]

So, the distance from boat to matt is 455.81535feet

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