To find the length of LS, you can use the Pythagorean theorem, which states:
\[ YL^2 = YS^2 + LS^2 \]
Given:
- \( YL = 15.4 \) km (hypotenuse)
- \( YS = 6.3 \) km (one leg)
You can substitute these values into the equation:
\[ (15.4)^2 = (6.3)^2 + LS^2 \]
Calculating the squares:
\[ 237.16 = 39.69 + LS^2 \]
Now, subtract \( 39.69 \) from both sides:
\[ LS^2 = 237.16 - 39.69 \]
\[ LS^2 = 197.47 \]
To find \( LS \), take the square root of both sides:
\[ LS = \sqrt{197.47} \approx 14.04 \text{ km} \]
Therefore, the length of \( LS \) is approximately 14.04 km.