Final answer:
By using the properties of similar triangles, the kite's height can be determined from the length of its string (9 feet) and the length of its shadow (7 feet). The calculated height of the kite is approximately 7.9 feet when rounded to the nearest tenth.
Step-by-step explanation:
To find the height of the kite, we must use the properties of similar triangles. The kite's string and height create a right triangle, and the shadow does the same on the ground with the peak of the kite's height at the top. Knowing that the string length is 9 feet, and the shadow casts 7 feet, we set up our triangles accordingly:
- The hypotenuse (the string) is 9 feet, which we know.
- The base (the shadow) is 7 feet.
Since the triangles are similar, the ratio of the kite's height to the shadow's length is the same as the ratio of the string's length to the kite's height:
Kite height / 7 ft = 9 ft / Kite height
Now, we solve for the kite's height by setting up an equation and squaring both sides to get rid of the fraction:
(Kite height)2 = (9 ft) x (7 ft)
(Kite height)2 = 63
Kite height = √63
Kite height ≈ 7.94 feet
Therefore, the height of the kite is approximately 7.9 feet (rounded to the nearest tenth).