To find out how far David is from his car after walking 50 yards north and 56 yards east, we can use the Pythagorean theorem. David's movement can be represented as a right triangle, with one leg measuring 50 yards (north) and the other leg measuring 56 yards (east).
The Pythagorean theorem states that:
\[ c = \sqrt{a^2 + b^2} \]
where
- \( c \) is the hypotenuse (the distance from the car),
- \( a \) is one leg of the triangle (50 yards),
- \( b \) is the other leg (56 yards).
Now, we can plug in the values:
\[ c = \sqrt{50^2 + 56^2} \]
Calculating \( 50^2 \) and \( 56^2 \):
\[ 50^2 = 2500 \quad \text{and} \quad 56^2 = 3136 \]
Now, add these values together:
\[ c = \sqrt{2500 + 3136} = \sqrt{5636} \]
Now, we calculate \( \sqrt{5636} \):
\[ \sqrt{5636} \approx 75.1 \]
Thus, rounding to the nearest tenth, the distance David is from his car is approximately:
\[ \boxed{75.1} \text{ yards} \]
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