Q1A. Elizabeth is flying a kite on a 90 feet string. The horizontal distance b/w Elizabeth and the Point

Thanks, geno.....another way to see this is that the sides are just multiples of a 6 -8 -10 Pythagorean Right Triangle.

Thus   9(6, 8, 10)   = 54 - 72 - 90      where 72 is the missing side we want

From Elizabeth (point A) to the point directly below the kite (pointC) and, from there up to the kite (point B) forms a right griangle with a right angle at C.

Using the Pythagorean Theorem:   c²  =  a² + b²

The distance from A to B is the hypotenuse, c:  c = 90.

The distance From A to C is one of the sides, b:  b = 54

The distance from C to B is the other side, a, the unknown.

c²  =  a² + b²     --->     90²  =  a² + 54²     --->     8100  =  a² + 2916     --->     5184  =  a²

--->   a  =  √5184     --->  a  =  72 ft