To find the length of LS given the lengths YS and YL, we can use the properties of a triangle and the given information, particularly the coordinates of points.
Let's denote:
- \( Y \) as the point at which the apex \( L \) connects lines to points \( S \) and \( Y \).
- \( S \) and \( L \) are points below point \( Y \).
From your question, we understand:
- \( YS = 6.3 \) km (the distance from \( Y \) to \( S \))
- \( YL = 15.4 \) km (the distance from \( Y \) to \( L \))
- \( L \) is the apex of the triangle.
Based on this information, we can create a right triangle where:
- \( YS \) forms one leg,
- \( YL \) forms another leg, and
- \( LS \) is the hypotenuse.
Using the Pythagorean theorem, which states that in a right triangle:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse (LS), and \( a \) and \( b \) are the lengths of the other two sides (Yl and Ys), we can plug in the values:
\[ LS^2 = YL^2 + YS^2 \]
Substituting the values:
\[ LS^2 = (15.4)^2 + (6.3)^2 \]
Calculating each term:
\[ (15.4)^2 = 237.16 \]
\[ (6.3)^2 = 39.69 \]
Now, combine these:
\[ LS^2 = 237.16 + 39.69 = 276.85 \]
To find \( LS \), we take the square root of both sides:
\[ LS = \sqrt{276.85} \approx 16.6 , \text{km} \]
Thus, rounding to the nearest tenth, the length of \( LS \) is approximately 16.6 km.
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