Question

If the rope is 8 feet long, about how far will the stake need to be from the middle of her tent?

Answer 1

- 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:

`Hypotenuse^2=Opposite^2+Adjacent^2`

- Thus, we can solve the question as follows:

`\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=√(48) \\ x=√(16*3) \\ x=4√(3)=6.92820...\approx6.9 \end{gathered}`

Final Answer

The answer is 6.9ft