Question

a camper attaches a rope to the top of her tent to give it more support. she stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. about how tall is her tent? 4.5 feet 10 feet 5.3 feet 6 feet

Explanation:

Step1: Identify the right triangle

The rope, the height of the tent, and the distance from the middle of the tent to the stake form a right triangle. The rope is the hypotenuse ($c = 8$ ft), the distance from the middle of the tent to the stake is one leg ($b = 6$ ft), and the height of the tent is the other leg ($a$), which we need to find.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right triangle, $a^2 + b^2 = c^2$. We can solve for $a$:

$a^2 = c^2 - b^2$

Substitute $c = 8$ and $b = 6$:

$a^2 = 8^2 - 6^2$

$a^2 = 64 - 36$

$a^2 = 28$

Step3: Solve for $a$

Take the square root of both sides:

$a = \sqrt{28}$

Simplify $\sqrt{28}$:

$\sqrt{28} \approx 5.3$ (since $5.3^2 = 28.09$, which is close to 28)

Answer:

5.3 feet (corresponding to the option "5.3 feet")