To find out how far David is from his car, we can use the Pythagorean theorem. David walked 34 yards north and 47 yards east, which forms a right triangle where:
- One leg (north) = 34 yards
- The other leg (east) = 47 yards
We can calculate the distance he is from his car (the hypotenuse) using the formula:
\[ c = \sqrt{a^2 + b^2} \]
where:
- \(a = 34\) yards
- \(b = 47\) yards
Now, we plug in the values:
\[ c = \sqrt{34^2 + 47^2} \]
Calculating \(34^2\) and \(47^2\):
\[ 34^2 = 1156 \] \[ 47^2 = 2209 \]
Now, we add these two values together:
\[ 1156 + 2209 = 3365 \]
Now take the square root of 3365:
\[ c = \sqrt{3365} \approx 58.0 \]
Thus, rounding to the nearest tenth, the distance David is from his car is approximately 58.0 yards.
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