If a point's ellipsoidal elevation is determined to be 592.8 ft and the geoid separation is -139.4 ft, what is the orthometric height above the geoid?

To determine the orthometric height above the geoid, you need to understand the relationship between ellipsoidal elevation, geoid separation, and orthometric height. The orthometric height (H) can be calculated using the formula:

H = Ellipsoidal Elevation - Geoid Separation.

In this scenario, the given figures are an ellipsoidal elevation of 592.8 ft and a geoid separation of -139.4 ft. When you plug these values into the formula, you find:

H = 592.8 ft - (-139.4 ft).

Since subtracting a negative value is the same as adding that value, the calculation simplifies to:

H = 592.8 ft + 139.4 ft = 732.2 ft.

Rounding it gives you 732 ft, making this height the orthometric height above the geoid. This value indicates how high the point is relative to the geoid rather than to the ellipsoid, which is particularly important in surveying and mapping applications where measurements need to be referenced to sea level or other geoid-related heights. The correct derivation and understanding of these relationships clarify that the computed orthometric height is 732 ft.