FE Civil Surveying Practice Problems

The current FE Civil specification assigns 6-9 of the 110 exam questions to Surveying. Form A contains 6 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A water main is to be laid from point A (N 1,200.00 m, E 800.00 m) to point B (N 950.00 m, E 1,100.00 m). The azimuth from north of line AB is most nearly:

(A)39.8°
(B)50.2°
(C)129.8°
(D)230.2°

Show worked solution

Answer: (C)

AB runs southeast ( $Δ N = - 250$ m, $Δ E = + 300$ m), so the $50.1 9^{\circ}$ bearing angle becomes azimuth $18 0^{\circ} - 50.1 9^{\circ} = 129. 8^{\circ}$ .

Inverse from A to B.

Δ N = 950.00 - 1200.00 = - 250.00 m

Δ E = 1100.00 - 800.00 = + 300.00 m

Departure over latitude gives the angle off the meridian.

θ = arctan (\frac{300.00}{250.00}) = 50.1 9^{\circ}

$Δ N < 0$ with $Δ E > 0$ places the line S 50.19° E; the azimuth folds back from 180°.

A z = 18 0^{\circ} - 50.1 9^{\circ} = 129. 8^{\circ}

FE Reference Handbook — Civil Engineering, Surveying: Coordinate Inverse (Azimuth from Latitudes and Departures)

Why the other choices appear

(A)Inverts the tangent ratio, computing arctan(250/300) = 39.8° and stopping without quadrant adjustment.
(B)Reports the reference angle 50.2° (the bearing angle) without converting to an azimuth in the southeast quadrant.
(D)Places the line in the southwest quadrant, computing 180° + 50.2° = 230.2° (sign error on the departure).