Question

If YS = 6.3 km and YL = 15.4 km, find the length of LS. Round your answer to the nearest tenth if necessary. You must show ALL work in order to receive full credit. You may type your work or use the button to insert a picture of your work.

Answer 1

To find the length of \( LS \) using the given information, we can apply the law of the triangle. Given that \( YS \) and \( YL \) are the distances from a point \( Y \) to points \( S \) and \( L \) respectively, we can deduce that \( LS \) can be calculated using the formula associated with a triangle, using Pythagoras' theorem if we consider that \( YS \) and \( YL \) form the two sides of a right triangle and \( LS \) would be the hypotenuse.

### Step 1: Define the lengths
We have:
- \( YS = 6.3 \, \text{km} \)
- \( YL = 15.4 \, \text{km} \)

### Step 2: Use the Pythagorean theorem
If triangle \( YSL \) is a right triangle with \( YS \) and \( YL \) as the legs, we can find the length of \( LS \) as follows:

\[
LS^2 = YS^2 + YL^2
\]

### Step 3: Calculate squares of \( YS \) and \( YL \)
First, calculate \( YS^2 \):
\[
YS^2 = (6.3)^2 = 39.69
\]
Next, calculate \( YL^2 \):
\[
YL^2 = (15.4)^2 = 237.16
\]

### Step 4: Add the squares
Now add these two results:
\[
LS^2 = YS^2 + YL^2 = 39.69 + 237.16 = 276.85
\]

### Step 5: Take the square root to find \( LS \)
Finally, take the square root to find \( LS \):
\[
LS = \sqrt{276.85} \approx 16.6 \, \text{km}
\]

### Conclusion
The length of \( LS \) is approximately \( 16.6 \, \text{km} \).