Question

David runs out of gas so he gets out of his car and walks 50 yards north and 56 blocks yards east. How far is he from his car if he walked back in a straight line? Round your answer to the nearest tenth.

Answer 1

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:

\[
\boxed{75.1} \text{ yards}
\]