A boy is flying a kite. The height of the kite is 1 1/2 times greater than the horizontal distance (x). The length of string that is out is 520 ft. Determine the height of the kite.
height^2+horizontal^2=length^2
(1.5 horizontal)^2+horizonal^2=520^2
horizontal^2*(2.25+1)=520^2
horizontal= 520/sqrt3.25
height= 1.5* horizontal= 1.5*520/sqrt3.25
check my work
To determine the height of the kite, we need to set up an equation using the given information.
Let's say the distance from the boy to the kite is x (in feet). According to the problem, the height of the kite is 1 1/2 times greater than the horizontal distance.
So, the height of the kite is (1 1/2) times x, which can be written as (3/2)x.
The length of the string that is out is given as 520 feet, which is equal to the hypotenuse (the diagonal line from the boy to the kite) in a right-angled triangle.
According to the Pythagorean theorem, in a right-angled triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, or the hypotenuse.
Using this information, we can form the equation:
x^2 + (3/2)x^2 = 520^2
Simplifying the equation, we get:
x^2 + (9/4)x^2 = 270,400
Combining like terms:
(13/4)x^2 = 270,400
To solve for x, we can multiply both sides by the reciprocal of 13/4, which is 4/13:
x^2 = (270,400) * (4/13)
x^2 = 82,880
Taking the square root of both sides, we find:
x = √82,880
x ≈ 287.746
Therefore, the horizontal distance (x) is approximately 287.746 feet.
To find the height of the kite, we can multiply this horizontal distance by (3/2):
Height = (3/2) * 287.746
Height ≈ 431.618 feet
Therefore, the height of the kite is approximately 431.618 feet.