# Thread: Law of sines word problem

1. ## Law of sines word problem

A ferris wheel has 16 evenly spaced cars. The distance between adjacent chairs is 15.5 ft. Find the radius of the wheel (to the nearest 0.1 ft).

I have no idea where to start..any help is appreciated!

2. Originally Posted by live_laugh_luv27
A ferris wheel has 16 evenly spaced cars. The distance between adjacent chairs is 15.5 ft. Find the radius of the wheel (to the nearest 0.1 ft).

I have no idea where to start..any help is appreciated!
If the cars are evenly spaced, then the angle between each radius is $\displaystyle \frac{360^{\circ}}{16} = 22.5^{\circ}$.

The distance between adjacent chairs is $\displaystyle 15.5\textrm{ft}$.

Let $\displaystyle r$ be the radius of the ferris wheel.

You now have an isosceles triangle with the equal lengths $\displaystyle r\textrm{ft}$ and the angle between them is $\displaystyle 22.5^\circ$.

Can you find the other two angles? Can you formulate a Sine Rule equation?

3. If you don't know the sine law, draw a perpendicular from the vertex of the isosceles triangle to the base so that you have two right triangles with "opposite side" of length 15.5/2= 7.75 feet, angle 22.5/2= 11.25 degrees, and hypotenuse of length r.

(I thought of doing this as a circle of circumference 15.5*16 but that is a digit off in the first decimal place.)