To find the length of the hypotenuse \( c \) in a right triangle with legs \( a \) and \( b \), you can use the Pythagorean theorem, which states:
\[ c^2 = a^2 + b^2 \]
Given:
- \( a = 3.4 \) kilometers
- \( b = 1.8 \) kilometers
First, we need to calculate \( a^2 \) and \( b^2 \):
\[ a^2 = (3.4)^2 = 11.56 \] \[ b^2 = (1.8)^2 = 3.24 \]
Now, add these two values:
\[ c^2 = a^2 + b^2 = 11.56 + 3.24 = 14.8 \]
Next, take the square root of both sides to find \( c \):
\[ c = \sqrt{14.8} \approx 3.844 \]
Finally, round to the nearest tenth:
\[ c \approx 3.8 \text{ kilometers} \]
Therefore, the length of the hypotenuse \( c \) is approximately 3.8 kilometers.