The first triangle has angles of 60 and 30 degrees with opposite sides of 4 and x, finding x to be 8 using trigonometric functions. The second triangle has angles of 25 and 63 degrees with opposite sides of 10 and x, finding x to be 6 using trigonometric functions. The third problem asks how far (x) a plane is from its landing spot, given the angle is 15 degrees and the opposite side is 800 feet, finding x to be 800/tan(15) = 1200 feet using trigonometric functions.