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Answer this question please very important
will give loads of points

Answer this question please very important will give loads of points-example-1
User Martin Dow
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Answer:

102.9 m

Explanation:

The shortest distance from A to C would be diagonally from A to C.

This comprises:

  • Two straight paths of equal length (shown in blue on the attached diagram).
  • Half the circumference of the central circle (shown in red on the attached diagram).

The length of the diagonal between A and C can be calculated using Pythagoras Theorem:


\begin{aligned}c^2&=a^2+b^2\\\implies \sf AC^2 & = \sf AB^2+AD^2\\\sf AC^2 & = \sf 50^2+80^2\\\sf AC^2 & = \sf 2500+6400^2\\\sf AC^2 & = \sf 8900\\\sf AC & = √(\sf 8900)\\\sf AC & = \sf 94.33981132\;m\end{aligned}

Subtract the diameter of the circular path from this to calculate the sum of the lengths of the straight paths.


\implies \sf 94.33981132-15=79.33981132\;m

To calculate the length of the circular part of the path, find half the circumference of the central circle:


\begin{aligned}\implies \textsf{Half the circumference} & = \sf (1)/(2) \pi d\\& =\sf (1)/(2) \pi (15)\\& =\sf 23.5619449\;m\end{aligned}

Therefore, the shortest distance from A to C across the park is:


\begin{aligned} \implies \textsf{Shortest distance} & = \sf 79.33981132+23.5619449\\& = \sf 102.9017562\\& = \sf 102.9\;m\;(nearest\:tenth)\end{aligned}

Answer this question please very important will give loads of points-example-1
User Sleep
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