To find out how far David is from his car after walking 171717 yards north and 454545 yards east, we can use the Pythagorean theorem. The northward distance and eastward distance can be considered the two legs of a right triangle, with the straight-line distance from his car being the hypotenuse.
Let:
- \( a = 171717 \) yards (north)
- \( b = 454545 \) yards (east)
The formula for the hypotenuse \( c \) is given by:
\[ c = \sqrt{a^2 + b^2} \]
Substituting the values:
\[ c = \sqrt{(171717)^2 + (454545)^2} \]
Calculating \( (171717)^2 \):
\[ (171717)^2 = 29471786709 \]
Calculating \( (454545)^2 \):
\[ (454545)^2 = 206626975025 \]
Now, adding the two results:
\[ a^2 + b^2 = 29471786709 + 206626975025 = 235098761734 \]
Now, taking the square root:
\[ c = \sqrt{235098761734} \approx 4850.4 \]
Therefore, rounding to the nearest tenth, David is approximately 4850.4 yards away from his car.
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