Final answer:
To find the length of a kite line with a 10-ft height and a 7-ft shadow, use the Pythagorean theorem. Calculate the square root of the sum of the squares of the height and the shadow to obtain the length of the hypotenuse, which is the kite line. The length is approximately 12.2 feet.
Step-by-step explanation:
The student's question involves finding the length of a kite's line when the kite is flying 10ft above the ground and casting a 7 ft shadow. This is a right-angled triangle problem where the height of the kite is one side of the triangle, the shadow is the base, and the kite line is the hypotenuse.
To solve for the length of the kite line, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (the kite line) is equal to the sum of the squares of the other two sides (the height of the kite and the length of the shadow). The formula is:
a² + b² = c²
Where a is the height of the kite (10ft), b is the length of the shadow (7ft), and c is the length of the kite line.
Substituting the values into the formula:
10² + 7² = c²
100 + 49 = c²
149 = c²
c = √149
c = 12.2 ft (rounded to the nearest tenth)
Therefore, the length of the kite line is approximately 12.2 feet.