Aradio station obtains a permit to increase the height of their radio tower on queen anne hill by no more than 100 feet. you are the head of the queen anne community group and one of your members asks you to make sure that the radio station does not exceed the limits of the permit. after finding a relatively flat area nearby the tower (not necessarily the same altitude as the bottom of the tower), and standing some unknown distance away from the tower, you make three measurements all at the same height above sea level. you observe that the top of the old tower makes an angle of 39° above level. you move 110 feet away from the original measurement and observe that the old top of the tower now makes an angle of 31° above level. finally, after the new construction is complete, you observe that the new top of the tower, from the same point as the second measurement was made, makes an angle of 40° above the horizontal. all three measurements are made at the same height above sea level and are in line with the tower. find the height of the addition to the tower to the nearest foot.