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.
Resolving Forces into Components: FE Civil practice problem 2
For the North Channel retaining wall replacement, a geotechnical reviewer preparing a basis-of-design update resolves a 280 lb cable force acting 35 degrees above horizontal. What is the horizontal component?
- A157.1 lb
- B184.6 lb
- C229.4 lb
- D204.5 lb
Show the answer and worked solution
Answer: C — 229.4 lb
Worked solution
- Step 1. Use the cosine component
F_x = F cos theta
- Step 2. Substitute values
F_x = 280 cos(35 deg) = 229.4 lb
Why the other choices are wrong
- Choice A
- This value is about 32% below the true horizontal component of 229.4 lb and does not come from one clean identifiable error like swapping sine for cosine or misreading the angle from vertical; the horizontal force still equals 280 lb * cos(35 deg), which gives 229.4 lb.
- Choice B
- This value is roughly 20% smaller than the actual horizontal component of 229.4 lb and cannot be traced to one clean error such as a degree-radian mix-up or a sine-cosine swap; the correct horizontal force is 280 lb * cos(35 deg), equal to 229.4 lb.
- Choice D
- This value runs about 11% below the correct horizontal component of 229.4 lb, and it does not follow from a standard single mistake such as using secant instead of cosine or applying the complementary angle; multiply 280 lb by cos(35 deg) directly to get 229.4 lb.