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Andrew is building a ramp for a snowboarding competition. The rules of the competition say that the height of the ramp must be 8 feet. Andrew has decided to make the base of the ramp and the piece of the ramp that forms the height meet at a 90° angle. The third piece of the ramp will be a straight line connecting the highest point of the ramp to the furthest point of the base, forming a 30° angle across from the 8 foot piece of the ramp. What will be the length of the third piece of the ramp? A. 16 feet B. 10 feet C. 13.86 feet D. 9.24 feet

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Answer:

The length of the third piece of the ramp is;

D. 9.24 feet

Step-by-step explanation:

The given parameters are;

The height of the ramp = 8 feet

The angle between the piece that forms height and the base = 90°

The angle formed by the third piece connecting the height of the ramp to the furthest point and the 8 foot piece = 30°

Let 'y' represent the 8-foot piece forming the height, and let 'r' represent the third piece, by trigonometric ratio, we have;

[tex]cos(30^{\circ}) = \dfrac{y}{r}[/tex]

Therefore, we get;

[tex]cos(30^{\circ}) = \dfrac{8}{r}[/tex]

[tex]r = \dfrac{8 \ feet}{cos(30^{\circ})} = \dfrac{8 \ feet}{\dfrac{\sqrt{3} }{2} } = \dfrac{16 \cdot \sqrt{3} \ feet}{3} \approx 9.24 \ feet[/tex]

The length of the third piece, r ≈ 9.24 feet

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