Using any Trigonometric definitions you will see hod to calculate an area of an oblique triangle using it's side lengths only

You can create a rectangle and triangle to solve for the area. The only problem is determining the height and base of the triangle. It just takes some trig.

Significant figures when multiplying or dividing uses the least significant count. In this case the least significant is 0.0023 which has only 2 significant figures (the 0's are place holders.)

Solve for the angle from top to bottom, then determine the distance from instrument to the top or bottom using law of sines. Then solve for right triangle. Don't forget about the instrument height!

There are a number of ways to determine the area. An easy way is to determine the area of the lot without the curve (7200 sq ft) then subtract a 20 x 20 square leaving 6800 sq ft. Then determine 1/4 the area of a 20' radius curve (314.1 sq ft) and add that back in.

This is linear algebra with two unknowns and two equations. You are looking to determine what x an y value will work for both equations. An easy way to do this is to rearrange the first equation to y = 6-2x and then replace y in the second equation so you have 4x-18+6x+8=0 and solve for x

Using the radius you can determine a circumference of 35,380.6 miles. Then set up a ratio of 360°/35,380.6 = X/2700. Don't forget to convert the answer to degrees minutes seconds

There are a number of ways to solve using linear algebra. An easy way is to rearrange the first equation so that 10x = 235 - 5y; then x = 23.5 - 0.5y. Replace x in the second equation so that you have 21(23.5-0.5y) + 9 y = 405. THis can be reduced to 1.5y = 88.5

This is a standard inverse question. Remember that Y values are Northings and that you are going south from A to E

The angular error would approximately equal the inverse tangent of how far off you were (0.5 inches) divided by the distance from the object (172 feet)