Use MATLAB, NGS Tools, and the data I have provided to answer the following questions.

The NGS tools can be found here: https://www.ngs.noaa.gov/TOOLS/

The data sheets can be found here: https://www.ngs.noaa.gov/NGSDataExplorer/

Please provide the MATLAB scripts and/or the NGS Outputs for each problem.

1. What is the difference between the published NAD 83 ellipsoid heights (h)?

2. What is the difference between the published Geoid 12 height (N)?

3. What is the NAVD 88 height (H) for each point derived from the published values for the ellipsoid height and geoid height using the equation: h - N = H. What is the difference between these values and the published values for the two monuments?

HL0445 C439 37 56 04.37050(N) 107 40 52.55829(W) 3008.183 2992.758 15.45 979,060.80 First, Class 2 447,754.079 N 722,673.299 E JL0618 A430 38 06 20.36122(N) 107 43 02.06315(W) 21945 2178.791 15.711 979,284.90 First, Class 2 466,814.754 N 719,962.643 E ELLIP H (02/10/07) 2178.813 ELLIP H (12/03/02) 2178.838 ELLIP H (03/16/99) 2178.807 0.6, 0.48, 3.37 -1,529,789,249 Y 4,788,488.251 Z 3,916,023.293 Designation NAVD83 (2011) Position (N,W) NAVD88 Height (m) Ellipsoid Height (m) Geoid Height (m) Modeled Gravity (mgal) Vertical Order and Class State Plane Coordinates CO S Previous Ellipsoid Heights (m ELLIP H (02/10/07) 2992.780 (m) ELLIP H (12/03/02) 2992.789 ELLIP H (03/16/99) 2992.796 0.61, 0.49, 3.92 X-_153053 1.659 Y -4,801,208.864 Z 3,901,556.369 Network Accuracy (N, E, Ellip) ECEF in meters (X,Y,Z) HL0445 C439 37 56 04.37050(N) 107 40 52.55829(W) 3008.183 2992.758 15.45 979,060.80 First, Class 2 447,754.079 N 722,673.299 E JL0618 A430 38 06 20.36122(N) 107 43 02.06315(W) 21945 2178.791 15.711 979,284.90 First, Class 2 466,814.754 N 719,962.643 E ELLIP H (02/10/07) 2178.813 ELLIP H (12/03/02) 2178.838 ELLIP H (03/16/99) 2178.807 0.6, 0.48, 3.37 -1,529,789,249 Y 4,788,488.251 Z 3,916,023.293 Designation NAVD83 (2011) Position (N,W) NAVD88 Height (m) Ellipsoid Height (m) Geoid Height (m) Modeled Gravity (mgal) Vertical Order and Class State Plane Coordinates CO S Previous Ellipsoid Heights (m ELLIP H (02/10/07) 2992.780 (m) ELLIP H (12/03/02) 2992.789 ELLIP H (03/16/99) 2992.796 0.61, 0.49, 3.92 X-_153053 1.659 Y -4,801,208.864 Z 3,901,556.369 Network Accuracy (N, E, Ellip) ECEF in meters (X,Y,Z)