# A wheel of a bicyle has a radius of 1.4 feet. Find the distance the bike travels when the wheel rotates through an angle of 150 degrees

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To solve apply the angular displacement formula which is:

`d=r theta`

where

d - linear displacement

r - radius of the curvature, and

`theta` - angular displacement in radians

But, before substituting the values to the formula, convert the given degrees to radians.

`150 ^o xx (pirad)/(180^o)=(5pi)/6` `rad`

Then, plug-in r=1.4 feet and `theta =(5pi)/6` radians to the formula.

`d=1.4*(5pi)/6=3.67`

**Hence, the distance travelled by the bike is 3.67 feet.**

I wheels rotate `2 pi` then the distance is `2pi r` r radius.

Since travel only `150^0 = 5/6 pi` then the travel is of `t=5/6 pi d=`

`=3.663 ft`