Final answer:
Using the Pythagorean theorem, the height of the pole determined as a right-angled triangle with the rope as the hypotenuse and the ground distance as one leg is approximately 8.7 yards when rounded to the nearest tenth.
Step-by-step explanation:
The question involves using the Pythagorean Theorem to find the height of the pole, which is connected to the ground via a 14-yard rope and touches the ground 11 yards from the base of the pole. We can consider this scenario as a right-angled triangle where the rope is the hypotenuse, the distance from the pole to where the rope touches the ground is one leg, and the height of the pole is the other leg.
To find the height of the pole, we use the Pythagorean theorem which is stated as a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. In this case, the length of the rope (“hypotenuse”) is 14 yards, and the distance from the pole to where the rope touches the ground (“one leg”) is 11 yards. Let's denote the height of the pole as h.
Applying the theorem:
11² + h² = 14²
121 + h² = 196
h² = 196 - 121
h² = 75
h = √75
h ≈ 8.7 yards (after rounding to the nearest tenth).
The height of the pole is approximately 8.7 yards.