the-circumference-of-a-circular-track-is-9-km-A-cyclist-rides-round-it-a-number-of-times-and-stops-after-covering-a-distance-of-302-km-How-far-is-the-cyclist-from-the-starting-point-take-22-7

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Question Number 43531 by pieroo last updated on 11/Sep/18

$$\mathrm{the}\mathrm{circumference}\mathrm{of}\mathrm{a}\mathrm{circular}\mathrm{track}\mathrm{is}9\mathrm{km}.\mathrm{A}\mathrm{cyclist}$$$$\mathrm{rides}\mathrm{round}\mathrm{it}\mathrm{a}\mathrm{number}\mathrm{of}\mathrm{times}\mathrm{and}\mathrm{stops}\mathrm{after}$$$$\mathrm{covering}\mathrm{a}\mathrm{distance}\mathrm{of}302\mathrm{km}.\mathrm{How}\mathrm{far}\mathrm{is}\mathrm{the}\mathrm{cyclist}$$$$\mathrm{from}\mathrm{the}\mathrm{starting}\mathrm{point}?[\mathrm{take}\mathrm{\Pi }=\frac{22}{7}]$$

Commented by pieroo last updated on 12/Sep/18

$$\mathrm{I}\mathrm{can}\mathrm{hardly}\mathrm{interprete}\mathrm{the}\mathrm{solution}.\mathrm{But}\mathrm{thanks}\mathrm{anyway}$$

Answered by MrW3 last updated on 11/Sep/18

$$302mod9=5kmor-4km$$$$2\pi R=9$$$$\Rightarrow R=\frac{9}{2\times \frac{22}{7}}=\frac{63}{44}km$$$$\theta R=4$$$$\Rightarrow \theta =\frac{4}{R}=\frac{176}{63}rad=160°$$$$L=2R\sin \frac{\theta }{2}=2\times \frac{63}{44}\times \sin 80°=2.82km$$$$\Rightarrow thecyclistis2.82kmfarfrom$$$$startingpoint.$$

Commented by MrW3 last updated on 12/Sep/18

Commented by MrW3 last updated on 12/Sep/18

$$A=startingpoint$$$$B=finishpoint$$$$L=\stackrel{\mathrm{\_}\mathrm{\_}}{AB}=distancebtw.AandB$$$$with\stackrel{⌢}{AB}=4km$$

Commented by pieroo last updated on 12/Sep/18

$$\mathrm{yea}\mathrm{its}\mathrm{clear}\mathrm{now}.\mathrm{thanks}\mathrm{very}\mathrm{much}$$

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