Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result, and the arithmetic was re-run as an executable calculation. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
Slope Distance to Horizontal Distance: FE Civil practice problem 5
During a constructability walkdown for the Fairview sewer siphon capital renewal project, the materials technician reduces a slope distance of 310 ft measured at vertical angle 2 degrees. What horizontal distance is obtained?
- A211.11 ft
- B249.44 ft
- C309.81 ft
- D335.30 ft
Show the answer and worked solution
Answer: C — 309.81 ft
Worked solution
- Step 1. Use horizontal projection
H = S cos theta
H = 310 cos(2 deg) = 309.81 ft
Why the other choices are wrong
- Choice A
- This result falls noticeably short of the horizontal distance that H = S cos(theta) yields for the given slope distance and vertical angle, and it does not match omitting the cosine reduction, swapping sine for cosine, or reading the complementary angle instead. Recompute using the slope distance times cos(theta) to reduce it to horizontal.
- Choice B
- This value is well above the horizontal-reduction result for the given slope distance and angle, and no single trig substitution or unit slip reproduces it cleanly. Use H = S cos(theta) with the stated slope distance and vertical angle to find the true horizontal distance.
- Choice D
- This figure sits above the horizontal distance obtained from the stated slope distance and vertical angle, and it doesn't reduce to a single recognizable slip such as dividing by the cosine or mixing up the vertical angle with its complement. The horizontal distance is the slope distance multiplied by cos(theta), nothing more.