Question

A camper attaches a rope from the top of her tent, 4
feet above the ground, to give it more support. If the rope is 8
feet long, about how far will the stake need to be from the middle of her tent?

Answer 1

To find out how far the stake needs to be from the middle of the tent, we can visualize the situation as a right triangle. The height of the tent where the rope attaches is 4 feet above the ground, and the length of the rope is 8 feet.

In this triangle:
- One leg represents the height from the ground to the point where the rope is attached (4 feet).
- The hypotenuse represents the length of the rope (8 feet).
- The other leg represents the horizontal distance from the base of the tent to the stake, which is what we want to find.

Using the Pythagorean theorem, we have:
\[
a^2 + b^2 = c^2
\]
where:
- \( a \) is the height (4 feet),
- \( b \) is the horizontal distance (the unknown),
- \( c \) is the length of the rope (8 feet).

Substituting the known values:
\[
4^2 + b^2 = 8^2
\]
\[
16 + b^2 = 64
\]
Now, we isolate \( b^2 \):
\[
b^2 = 64 - 16
\]
\[
b^2 = 48
\]
Now, taking the square root of both sides:
\[
b = \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \approx 6.93
\]

Thus, the stake needs to be approximately **6.93 feet** from the middle of the tent.