Question

Santos walks 2 kilometers south and then a certain number of kilometers east. he ends 5 kilometers away from his starting position.

how many kilometers east did santos walk?
round your answer to the nearest tenth of a km.

___km

Answer 1

To determine how many kilometers east Santos walked, we can use the Pythagorean theorem.

Santos walked 2 kilometers south and some distance \( x \) kilometers east. He ended up 5 kilometers away from his starting position, which serves as the hypotenuse of a right triangle where one leg is 2 kilometers (south direction), and the other leg is \( x \) kilometers (east direction).

According to the Pythagorean theorem, we have:

\[
a^2 + b^2 = c^2
\]

Where:
- \( a \) is the distance walked south (2 km),
- \( b \) is the distance walked east (\( x \) km),
- \( c \) is the distance from the starting point (5 km).

Substituting the known values into the equation, we get:

\[
2^2 + x^2 = 5^2
\]

Calculating the squares:

\[
4 + x^2 = 25
\]

Next, we solve for \( x^2 \):

\[
x^2 = 25 - 4
\]
\[
x^2 = 21
\]

Now, we take the square root to find \( x \):

\[
x = \sqrt{21} \approx 4.5826
\]

Rounding to the nearest tenth, we find that:

\[
x \approx 4.6 \text{ km}
\]

Thus, Santos walked approximately **4.6 kilometers** east.