An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ turn to the right and walks 4 more feet. It then makes another 160^ turn to the right and walks 4 more feet. If the ant

Correct answer: 36 aligned & Let A_0(0,0) & A_1(4 0,4 0) & A_2(4 0+4 160,4 0+4 160) & A_n=(0,0) & 4( 0+ 160+ . .+ 160(n-1))=0 and 4( 0+ 160+ . .+ 160(n-1))=0 & (80 n)=0 & n=9 & distance covered =4 × 9=36 feet aligned

Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Straight Lines

Olympiad workbook · IOQM · Straight Lines

An ant leaves the anthill for its morning exercise. It walks 4 feet...

An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a

160^{\circ}

turn to the right and walks 4 more feet. It then makes another

160^{\circ}

turn to the right and walks 4 more feet. If the ant continues this pattern until it reaches the anthill again, what is the distance in feet it would have walked? An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ turn to the right and

An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ turn to the right and

Correct answer

Step-by-step solution

\begin{aligned} & \text { Let } A_0(0,0) \\ & A_1(4 \cos 0,4 \sin 0) \\ & A_2(4 \cos 0+4 \cos 160,4 \sin 0+4 \sin 160) \\ & A_n=(0,0) \\ & \Rightarrow 4(\cos 0+\cos 160+\ldots . .+\cos 160(n-1))=0 \text { and } 4(\sin 0+\sin 160+\ldots . .+\sin 160(n-1))=0 \\ & \Rightarrow \sin (80 n)=0 \\ & \Rightarrow \mathbf{n}=\mathbf{9} \\ & \Rightarrow \text { distance } \text { covered }=4 \times 9=36 \text { feet }\end{aligned}

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