Question

Igor is flying a kite. The kite is 170m off of the ground. The string of the kite and the line parallel to the ground form an angle of 68 degrees. Igor is holding the kite 1 m off of the ground. Approximately how much string has Igor let out?

Answer 1

looks like you are involving hypotenuse and opposite, so sine.
sin 68° = 169/string
string = 169/sin68 = ....

Answer 2

sin68°= 170/x
x=170/sin68°
x=183.4

Igor has let out 183.4m or 183m of string.