The height of Mount Everest was originally measured by a surveyor in the following way. He first measured the altitudes of two points and the horizontal distance between them. For example, suppose that the points A and B are 3000 m above sea level and are 10,000 m apart. He then used a theodolite to measure the direction cosines of the vector rAP from point A to the top of the mountain P and the vector rBP from point B to P. Suppose that the direction cosines of rAP are cos θx = 0.5179, cos θy = 0.6906, and cos θz = 0.5048, and the direction cosines of rBP are cos θx = 0.3743, cos θy = 0.7486, and cos θz = 0.5472.
1. Using this data, determine the height of Mount Everest above sea level