If YS = 6.3 km and YL = 15.4 km, find the length of LS. for other context YL is the hypotenuse YS is a leg and SL is the other leg

1 answer

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.