Final answer:
The height of the kite is 700 feet and the length of the string is approximately 763.93 feet.
Step-by-step explanation:
To find the height of the kite, we can use the slope of the string. The slope of the string represents the vertical change divided by the horizontal change. In this case, the slope is 7/3, which means for every 3 feet horizontally, the string rises 7 feet vertically. Since the kite is 300 feet horizontally from Franklin's hands, the vertical distance is (7/3) * 300 = 700 feet. Therefore, the height of the kite is 700 feet.
The amount of string between the kite and Franklin's hands is equal to the hypotenuse of a right triangle formed by the horizontal and vertical distances. We can use the Pythagorean theorem to find the length of the string. The formula is c^2 = a^2 + b^2, where c is the length of the string, a is the horizontal distance, and b is the vertical distance. Plugging in the values, we get c^2 = 300^2 + 700^2. Solving for c, we find that the length of the string is approximately 763.93 feet. Therefore, the correct answer is d) 800 feet.