Solution
- In order to solve the question, we simply need to apply Pythagoras theorem.
- The Hypotenuse of the right-angled triangle formed by the whole set up is given by the rope's length.
- The Opposite of the right-angled triangle formed is given by the height of the tent.
- The distance from the center of the tent to the point where the rope touches the ground is what we are looking for. Let it be x.
- The Pythagoras theorem is given as:
[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
- Thus, we can solve the question as follows:
[tex]\begin{gathered} Hypotenuse=8,Opposite=4,Adjacent=x \\ \\ 8^2=4^2+x^2 \\ 64=16+x^2 \\ \text{ Subtract 16 from both sides} \\ \\ x^2=64-16 \\ x^2=48 \\ \text{ Take the square root of both sides} \\ \\ x=\sqrt{48} \\ x=\sqrt{16\times3} \\ x=4\sqrt{3}=6.92820...\approx6.9 \end{gathered}[/tex]
Final Answer
The answer is 6.9ft
