FE Civil · Chapter 10 · 4–6 exam questions

FE Civil Surveying

This chapter covers angles, bearings, and distances; differential leveling; traverse computations; area and volume calculations; and horizontal and vertical curve design — the core surveying topics tested on the FE Civil exam.

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What the FE tests in Surveying

Measurement & Leveling

As a civil engineer, every project starts with measuring angles, distances, and elevations. You convert between bearings and azimuths, run level loops to establish grades for drainage, and close traverses to verify accuracy. Getting the survey wrong means the entire design is wrong — from building pad elevations to sewer inverts.

Area, Volume & Traverse

As a civil engineer, you compute traverse closures to verify boundary surveys, use the coordinate method to determine property areas and impervious surface coverage, and calculate earthwork volumes for cut-and-fill estimating. These computations directly affect project costs, regulatory compliance, and legal property descriptions.

Horizontal & Vertical Curves

As a civil engineer, you design horizontal curves to provide adequate sight distance and superelevation for the design speed, and vertical curves to ensure stopping sight distance over crests and headlight illumination through sags. Curve geometry determines lane widths, right-of-way requirements, and grading quantities.

Key Surveying formulas

$\text{Lat} = L\cos\theta, \quad \text{Dep} = L\sin\theta$
Traverse Lat/DepFE Handbook p. 309
$A = \frac{1}{2}|\sum(x_i y_{i+1} - x_{i+1} y_i)|$
Coordinate AreaFE Handbook p. 310
$V = \frac{L}{2}(A_1 + A_2)$
Average End AreaFE Handbook p. 309
$V = \frac{L}{6}(A_1 + 4A_m + A_2)$
Prismoidal FormulaFE Handbook p. 309
$T = R\tan\frac{I}{2}$
Horizontal Curve TangentFE Handbook p. 302
$D = \frac{5{,}729.58}{R}$
Degree of CurveFE Handbook p. 302
$Y = Y_{PVC} + g_1 x + \frac{g_2 - g_1}{2L}x^2$
Vertical Curve ElevationFE Handbook p. 301
$L = \sqrt{\Delta E^2 + \Delta N^2}, \; Az = \tan^{-1}\!\frac{\Delta E}{\Delta N}$
Inverse Computation (distance & azimuth)

Sample Surveying problems

Q1. A surveyor measures a bearing of N 45° E from point A to point B, a distance of 200 m. What is the northing (latitude) of point B relative to A?

Answer: 141.4 m

Explain it simply

The latitude (northing) is the north-south component: distance times cosine of the bearing angle. $\text{Lat} = 200 \cos 45° = 200 \times 0.7071 = 141.4$ m. The departure (easting) would be $200 \sin 45° = 141.4$ m too, since it is a 45-degree bearing. Common trap is mixing up which trig function gives latitude vs departure.

Q2. The bearing S 30° W is equivalent to which azimuth?

Answer: 210°

Explain it simply

S 30° W means 30 degrees west of due south. Due south is 180° azimuth. Going 30 degrees toward west (clockwise from north) gives $180 + 30 = 210°$ . The key is remembering that azimuth is measured clockwise from north (0°/360°).

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Common Surveying mistakes on the FE

Mixing up backsight and foresight in differential leveling — BS is added, FS is subtracted from the HI.
Forgetting to close the traverse — always check that latitudes and departures sum to zero.
Using the wrong formula for curve length — horizontal curves use L = πRI/180, vertical curves use station difference.
Confusing azimuth (from north, clockwise, 0–360°) with bearing (from N or S, toward E or W, 0–90°).
Assuming the high/low point of a vertical curve is at the midpoint — it’s only true when |g_1| = |g_2|.
Forgetting to divide by 2 in the coordinate area formula — doubles your answer.
Departure = E-W = L·sin(Az); latitude = N-S = L·cos(Az) — sine with easting, cosine with northing.
The arctangent alone cannot fix an azimuth's quadrant — use the signs of ΔE and ΔN.

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