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The paris fire department is called to fight a 3 story apartment fire.The ladder on the fire truck expands 55ft at an angle of 72.In order for the ladder to reach the top of the building, how close does the firetruck need to be from the base of the building rounded to the nearest whole foot.

Answer :

The situation is:

We need to find the length of the green line.

This is a right triangle, and we know the measure of the hyppotenuse, and an angle.

We can use the trigonometric relation cosine to find the distance from the firetruck to the building:

[tex]\cos \theta=\frac{\text{adjacent leg}}{hyppotenuse}[/tex]

The distance between the truck and the buiding is the adjacent leg to the angle, let's call it x, then:

[tex]\cos (72º)=\frac{x}{55ft}[/tex]

And we can solve for x:

[tex]\begin{gathered} \cos (72º)\cdot55ft=x \\ x=0.309\cdot55ft=16.995ft \end{gathered}[/tex]

To the nearest whole foot, the distance between the firetruck and the building to reach the top of the building is 17ft

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