To solve the problem of finding the height of the kite from the ground, we can utilize the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (in this case, the string) is equal to the sum of the squares of the other two sides.
Here, the boy, the kite, and the ground form a right triangle where:
- The length of the string (hypotenuse) is 20 meters.
- The horizontal distance between the boy and the kite is 15 meters.
- The height of the kite from the ground is the vertical side we need to find.
Let's denote:
- [tex]\( s \)[/tex] as the length of the string (hypotenuse), [tex]\( s = 20 \)[/tex] meters.
- [tex]\( d \)[/tex] as the horizontal distance, [tex]\( d = 15 \)[/tex] meters.
- [tex]\( h \)[/tex] as the height of the kite from the ground, which we need to determine.
According to the Pythagorean theorem:
[tex]\[ s^2 = d^2 + h^2 \][/tex]
Plugging in the known values:
[tex]\[ 20^2 = 15^2 + h^2 \][/tex]
[tex]\[ 400 = 225 + h^2 \][/tex]
To find [tex]\( h^2 \)[/tex], we isolate it:
[tex]\[ h^2 = 400 - 225 \][/tex]
[tex]\[ h^2 = 175 \][/tex]
Thus, the height ([tex]\( h \)[/tex]) is:
[tex]\[ h = \sqrt{175} \][/tex]
Therefore, the height of the kite from the ground is:
[tex]\[ \sqrt{175} \, \text{meters} \][/tex]
The correct answer is:
D) [tex]\( \sqrt{175} \, \text{m} \)[/tex]
