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6. The swing set on the playgrounds is getting wobbly, and you have been asked to put outrigger boards to help stabilize it. If the crossbar of the swing is 10 feet off of the ground, the outrigger to be attached at a 40 degree angle, and you want to bury the outrigger boards 3 feet onto the ground, how long would the boards have to be? (Hint: the outrigger is the hypotenuse of a right triangle)

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okpalawalter8

Answer:

[tex]X=18.6ft[/tex]

Step-by-step explanation:

From the question we are told that:

Height of swing's crossbar [tex]H=10ft[/tex]

Angle [tex]\theta=40 \textdegree[/tex]

Depth of outrigger [tex]d_=3ft[/tex]

Generally the equation for slant height l is mathematically given by

[tex]l=\frac{opposite}{sin\theta}[/tex]

Therefore

[tex]l=\frac{H}{sin\theta}[/tex]

[tex]l=\frac{10}{sin 40\textdegree}[/tex]

[tex]l=15.6ft[/tex]

Since the Depth of outrigger

[tex]d_=3ft[/tex]

Therefore Length of the board X

[tex]X=l+d[/tex]

[tex]X=15.6+3[/tex]

[tex]X=18.6ft[/tex]

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