Question

A camper attaches a rope from the top of her tent, feet above the ground, to give it more support. If the rope is feet long, about how far will the stake need to be from the middle of her tent?

Answer 1

Given that

The height of the tent is 4 feet and the length of the rope is 8 feet.

We have to find the distance of the rope from the tent.

Explanation -

The given diagram is

Here the given diagram is making a right-angled triangle.

So we will use the Pythagoras theorem to find the required length.

The Pythagoras theorem is given as

$\begin{gathered} H^2=P^2+B^2 \\ \\ where\text{ H = hypotenuse, B = base, and P = perpendicular} \end{gathered}$

Here Hypotenuse = H = 8 feet, Base = B = ?, and Perpendicular = P = 4 feet.

Then,

$\begin{gathered} 8^2=4^2+B^2 \\ B^2=8^2-4^2=64-16 \\ B^2=48 \\ B=\sqrt{48} \\ B=\sqrt{2\times2\times2\times2\times3} \\ B=2\times2\times\sqrt{3} \\ B=4\sqrt{3}\text{ feet} \\ \\ As\text{ }\sqrt{3}=1.732 \\ \\ B=4\times1.732\text{ feet} \\ B=6.928\text{ feet} \end{gathered}$

So the required distance will be 6.928 feet.

Hence, C is the correct option.

Final answer -

Therefore the final answer is 6.928