The height of the observer can be taken negligible in case of big measurements. The height of the kite from the ground is 40 meters approximately.
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Referring to the figure attached below, we have the vertical distance of the kite from the ground as the length of the side BC.
(assume that the height of the observer flying kite is negligible and that kite's string is straight, and some more basic assumptions)
Using the Pythagoras theorem as the triangle ABC is a right angled triangle as vertical distance means line perpendicular to the ground, we get the length of the line segment BC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|BC|^2 = |AC|^2 - |AB|^2\\\\|BC| = \sqrt{|AC|^2 - |AB|^2}\\[/tex]
(positive root since length is a non-negative quantity).
We have |AC| = length of the kite's string = 50 meters
|AB| = distance of the observer from the point directly above which the kite is flying = 30 meters
Thus, we get the height of the kite from the ground as:
[tex]|BC| = \sqrt{|AC|^2 - |AB|^2}\\|BC| = \sqrt{50^2 - 30^2} = \sqrt{1600} = 40\: \rm \text{(in meters)}[/tex]
Thus, the height of the kite from the ground is 40 meters approximately.
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
