Question

A small-scale Ferris wheel is constructed for a children's park with six cars, as shown.The segments connecting the cars are twelve feet long, and the segments connectingthe center to each car are also twelve feet long. Support beams are added from thecenter of the Ferris wheel to the center of each segment connecting the cars. Thesesupport beams are perpendicular to the segments connecting the cars. What is thelength of each support beam? Round to the nearest tenth.12 ft.13.4 ft.6 ft.12 ft.17.0 ft.10.4 ft.A

Answer 1

Notice that equilateral triangles with side 12ft are created, and the support beams take those equilateral triangles apart on two right-triangle shaped parts:

Use the Pythagorean Theorem to find the value of x:

`\begin{gathered} x^2+(6ft)^2=(12ft)^2 \\ \Rightarrow x^2+36ft^2=144ft^2 \\ \Rightarrow x^2=144ft^2-36ft^2 \\ \Rightarrow x^2=108ft^2 \\ \Rightarrow x=\sqrt[]{108ft^2} \\ \Rightarrow x=10.4ft \end{gathered}`

Therefore, the answer is:

`10.4ft`