Question

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 and L is the apix

Answer 1

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**.