Akite is being flown at a 45° angle with the ground. the length of the string between the person and the kite is 100 ft. long. how high is the kite vertically above the point at which the string is being held?

For this case you can see the problem like a triangle with a right angle (90 degrees), an angle of 45 degrees and a hypotenuse of 100 feet.
 Then, the vertical height above the point where the rope is held is
 y = 100 * sin (45) = 70.71 ft
 The answer is
 the kite vertically above the point at which the string is being held is 70.71 ft high

In the given, we can form a right triangle out of the person and the kite. The distance between the person and the kite, which is given to be 100 ft is equal to the hypotenuse. The vertical distance can be calculated through the equation,

        H = (100 ft)(cosine 45°)

Simplifying,

       H = 70.71 ft

70.71 ft

Neither is the answer