A girl lets out 50 yards of kite string while flying a kite. The distance from a point on the ground directly under the kite to where the girl is standing is 30 yards. If the girl holds the string 3 feet from the ground,how high is the kite? Assume the string is tight.
a boy is flying a kite and lets out 80 meters of string.the horizontal distance along the ground from the boy to a point directly the kite is 30 meters.what is the angle of elevation?
To find the height of the kite, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this scenario, the hypotenuse represents the distance from the girl to the kite, the shorter side represents the height of the kite, and the longer side represents the distance from the girl to the point directly under the kite.
Given that the girl lets out 50 yards of kite string, and the distance from the point under the kite to where the girl is standing is 30 yards, we can determine the length of the hypotenuse:
Hypotenuse = √(height^2 + distance^2)
Hypotenuse = √(50^2 + 30^2) yards
Hypotenuse = √(2500 + 900) yards
Hypotenuse = √3400 yards
Now, we need to convert the hypotenuse from yards to feet, as the height is given in feet. Since 1 yard is equal to 3 feet:
Hypotenuse = √3400 yards * 3 feet/yard
Hypotenuse ≈ √(3400 * 3) feet
Hypotenuse ≈ √10200 feet
Hypotenuse ≈ 101 feet
Since the girl holds the string 3 feet from the ground, the height of the kite can be calculated by subtracting 3 feet (the distance from the ground to the girl's hand) from the hypotenuse:
Height = Hypotenuse - 3 feet
Height ≈ 101 feet - 3 feet
Height ≈ 98 feet
Therefore, the kite is approximately 98 feet high.