A teenager in a highrise building looks out his window at another building across the street and realizes a crime is being committed. If the buildings are 60 feet apart, and the teenager is looking down into the other building with an angle of depression of 20°, how many feet lower is the floor where the crime is being committed? If each floor is 10 feet, about how many floors down is it?

Respuesta :

Hello!

The first step to solving this exercise is to draw the situation, look:

Now we can solve this exercise. Notice that we want to know the height that I called "X".

To find it, we must use the tangent of 20º, look:

[tex]\tan (20\degree)=\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} \frac{0.364}{1}=\frac{60}{x} \\ \\ 0.364x=60 \\ x=\frac{60}{0.364} \\ \\ x\cong164.83 \end{gathered}[/tex]

If each floor is 10 feet:

[tex]\frac{164.83}{10}=16.483\text{ floors}[/tex]

If you have to approximate, you can say that it is 16.5 floors down.

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