In the above figure, let A be the position of the kite. Draw a perpendicular AB from A onto the ground. Since there is no slack in the string, so we can take AC = 100 m to be the string, where C is the position where the string touches the ground. Also, the string makes an angle of 60° with the horizontal. Join B and C. So we get a right-angled triangle ABC with right angle at B and ∠ACB = 60°. We have to find the height of the kite from the ground, that is, AB.

or,

or,

Hence the correct choice is A.