The angles of elevation to a balloon in the air from two points on level ground are 27 degrees and 45 degrees. If the points are 9 miles apart and the balloon is between the 2 points, in the same vertical plane, approximate, to the nearest tenth of a mile, the height of the balloon above ground.

As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag. first the players must decide who is playing black marbles and who is playing red marbles. then each player takes a turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting the color before returning it to the bag. the point scheme for the game is detailed in the table below. point values for marble game black marble points red marble points both black: +2 points both red: +4 points different colors: –1 point different colors: –1 point both red: 0 points both black: 0 points