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
