Compute projection scale factor, Mathematics

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1. A survey line on campus is measured to be 1000.00 ft long on horizontal ground. The elevation of the line is 700.00 feet and the geoid separation from ellipsoid to geoid is -110.00 feet.  If the radius of the ellipsoid is 20,906,000.00 feet, what is the elevation factor for this line to 8 gnificant digits?  What is the geodetic length of the line on the ellipsoid to the nearest 0.01 feet?

2. Given Ground length of line GH = 24681.334 m

Geodetic length of line GH = 24680.721 m

Grid length of line GH = 24679.584 m

a. Compute elevation factor for line GH to 8 gnificant digits.

b. Compute projection scale factor for line GH to 8 gnificant digits.

3. The area of a triangle is given by A = ½ ab sin θ

Given the following measurements:

a = 400.00 ft Fa = ±0.05 ft

b = 650.00 ft Fb = ±0.08 ft

2 = 35° 50' F2 = ±30 sec

a. Sketch and the triangle and label.

b. Compute the area of the triangle to the nearest 0.1 square feet.

c. Using the error propagation equation, compute the contribution of each measured variable to the uncertainty in the area (standard deviation F).  Which variable contributes the most to the uncertainty.  Be careful to not mix units.

d. Compute the total error in the computed area.

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