Answer
Distance between two tracking stations is\[\text{6 Km}\].
Work Step by Step
A rocket is being launched from a point C which is a midway between two tracking stations (i.e., at point B and Point D) on the ground. When rocket reaches point A which is 4 Km above the ground, it becomes 5 Km away from each station.
Let c be the distance from point A to point B, b be the distance from point C to point B and \[a\] be the distance from point C to point A.
Hence\[c=5\],\[a=4\] and\[b=BC\].
Compute value of \[c\]by using Pythagorean Theorem in \[\Delta ACB\] and by using formula
\[\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}} \\
& {{5}^{2}}={{4}^{2}}+B{{C}^{2}}
\end{align}\]
Now if\[{{5}^{2}}=5.5=25\]and \[{{4}^{2}}=4.4=16\] then solve the equation as shown below.
\[25=16+B{{C}^{2}}\]
Subtract 16 from both sides to compute x as shown below.
\[\begin{align}
& 25-16=B{{C}^{2}} \\
& 9=B{{C}^{2}} \\
& \sqrt{9}=B{{C}^{2}} \\
& 3=BC
\end{align}\]
Compute the distance between two stations is shown by point B and point D using the equation as shown below.
\[\begin{align}
& BD=BC+CD \\
& =3\text{ Km}+3\text{ Km} \\
& =6\text{ Km}
\end{align}\]
Distance between two tracking stations is\[\text{6 Km}\].
