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Answer :
Use Pythagorean theorem
a^2 + b^2 = c^2
6^2 + 9^2 = c^2
36 + 81 = c^2
117 = c^2
c = 10.8 miles
a^2 + b^2 = c^2
6^2 + 9^2 = c^2
36 + 81 = c^2
117 = c^2
c = 10.8 miles
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Final answer:
The shortest distance the runner must travel to return to their starting point is approximately 10.8 miles.
Explanation:
To find the shortest distance the runner must travel to return to their starting point, we can use the Pythagorean theorem. The north and east distances form a right triangle, with the shortest distance being the hypotenuse. So, we can calculate the shortest distance using the formula:
Shortest distance2 = (North distance)2 + (East distance)2
Plugging in the given north distance of 9 miles and east distance of 6 miles, we get:
Shortest distance2 = 92 + 62
Shortest distance2 = 81 + 36
Shortest distance2 = 117
Taking the square root of both sides, we find that the shortest distance is approximately 10.8 miles to the nearest tenth of a mile.
Learn more about Pythagorean theorem here:
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