Question

question id: 109879
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
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?
○ 5.3 feet
○ 10 feet
○ 4.5 feet
○ 6 feet

Explanation:

Step1: Identify right triangle sides

The rope (8 ft) is the hypotenuse, the horizontal distance (6 ft) is one leg. Let the tent height be $h$.

Step2: Apply Pythagorean theorem

$$h^2 + 6^2 = 8^2$$

Step3: Calculate squared terms

$$h^2 + 36 = 64$$

Step4: Isolate $h^2$

$$h^2 = 64 - 36 = 28$$

Step5: Solve for $h$

$$h = \sqrt{28} \approx 5.3$$

Answer:

5.3 feet