In order to find "n", you need to isolate it. So you would subtract 52 from both sides. You have 23+n=-36. Now, you subtract 23 from both sides. You have n=-59. Do you need any more clarification?
Taking the length of the string to be the hypothenuse and the vertical height above the ground to be the 'opposite' side, the length of the string = 70/sin(40°) = 109 feet