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 î¸x = 0.5179, cos î¸y = 0.6906, and cos î¸z = 0.5048, and the direction cosines of rbp are cos î¸x = 0.3743, cos î¸y = 0.7486, and cos î¸z = 0.5472.
1. using this data, determine the height of mount everest above sea level