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For a right triangle the square of hte hypotenuse side is equal to the sum of the square of the other two sides.
The length of the straight line distance from the starting point to the end point is 11.4 miles. (to the nearest tenth)
According to Pythagoras theorem for a right angle triangle the square of the length of the hypotenuse is equal to the sum of the square of the other two sides of that right triangle.
Given information-
Total driving in the west direction is 3 miles.
Total driving in the north direction is 11 miles.
As the driving in the straight direction makes a right angle. In this right angle the shortest path will be hypotenuse of the triangle as shown in the image.
Let suppose the shortest distance from starting point to end point is x miles.
Thus by the Pythagoras theorem,
[tex]x^2=3^2+11^2\\x^2=9+121\\x^2=130\\x=\sqrt{130}\\x=11.402[/tex]
Hence the length of the straight line distance from the starting point to the end point is 11.4 miles. (to the nearest tenth).
Learn more about the Pythagoras theorem here;
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