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Elementary Geometry For College Students, 7e

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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An xyz-coordinate system is placed with its origin at the center of the earth, so that the equator is in the xy-plane, the North Pole has coordinates (0, 0, 3960), and the xz-plane contains the prime meridian, which is the great semicircle that runs through Greenwich, England on its way from the North Pole to the South Pole. Recall that the y-axis is oriented so that it points east, into the Indian Ocean. Find the coordinates (x,y,z) of Exeter NH, whose latitude and longitude are 43 degrees north and 71 degrees west.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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At a ski resort, the highest ski run, Hattie’s Haven, can only be accessed by taking two lifts. The first lift leaves the lodge area and travels 1200 m at an inclination of 43° to a transfer point. From the transfer point, the new lift travels 1500 m at an inclination of 53° to the top of Hattie’s Haven ski run. The resort is undergoing renovations and is planning on creating a new ski run called Giffin’s Gallop. This run would be 30 m to the right of the top of Hattie’s Haven and 40 m higher. A new lift must be installed that goes directly from the lodge area to the top of Giffin’s Gallop. Determine the angle of elevation of the lift from the lodge area to the top of Giffin’s Gallop
An observer at Point A makes measurements that show that the peak of Mount Wayne lies in a direction of 50 degrees from Point A, with an angle of elevation of18 degrees. The peak of Mount Rolly lies in a direction of 340 degrees from Point A, with an angle of elevation of 23 degrees. The peak of Mount Maggie lies in a direction of 190 degrees from Point A, at an angle of elevation of 13 degrees. The distance to the peak of Mount Wayne is 2980 m. The distance to the peak of Mount Rolly is 3450 m. The distance to the peak of Mount Maggie is 5130 m.1. Determine the horizontal distance from point A to each mountain peak.2. State a position vector for each mountain peak, relative to point A.3. A helicopter takes off from Point A, travels to the peak of Mount Wayne, then tothe peak of Mount Rolly, then flies halfway to the peak of Mount Maggie, and landson a ridge at an altitude of 300 m higher than Point A. Determine the resultant vectorof the total flight.4. If the average speeds of the…

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