FE exam Math – Law of Cosines Explained |

Struggling with triangle problems on the FE Civil Exam? Let’s solve this Law of Cosines question step by step — exactly how it appears in the FE Reference Handbook (Mathematics: Trigonometry Section, Page 23).

In this video, we’ll find angle A of a triangle with sides a = 780 ft, b = 960 ft, and c = 1440 ft, using the Law of Cosines formula: cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)
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00:00 Introduction to Law of Cosines Problem
00:22 Identifying Sides of a Triangle
00:38 Using the FE Reference Manual
00:46 Law of Cosines Formula Explained
00:56 Solving for the Unknown Angle

We’ll cover:
✅ Step-by-step solution process
✅ Substitution and simplification
✅ Using your calculator correctly for the FE Exam
✅ How to find angles in degrees using arc cos (inverse cosine)
✅ Common FE Exam mistakes to avoid

By the end, you’ll understand how to apply cosine law confidently to any FE-style trigonometry question.

📘 Reference:
Mathematics – Trigonometry Section, FE Reference Handbook, Page 23

📊 Problem Type: FE Civil – Trigonometry / Geometry
🧮 Formula Used: Law of Cosines
🎯 Difficulty Level: Moderate

RESOURCES & LINKS MENTIONED IN THIS VIDEO:
BOOKS RECOMMENDED FOR THE FE:
FE Civil Practice Exam NCEES:
https://amzn.to/2Ue5YgK
FE Civil Reference Manual: (FREE Signup/Signin and use link to DOWNLOAD)
https://account.ncees.org/reference-h...
FE Civil Practice (Latest edition):
https://amzn.to/2UOPCiV
FE Civil Practice Problems (Oldest edition):
https://amzn.to/2X1BY9R
TI-36X Pro:
https://amzn.to/2IrJsPm
TI 84 Plus Graphing Calculator:
https://www.amazon.com/Graphing-Calcu...

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⏱️ Chapters (With Hooks & Tags)

00:00 - Introduction to the Problem
01:08 - Understanding Pressure Distribution (Pressure Triangle)
01:30 Pressure Formula: P = ρ * g * H
02:20 Calculating Average Pressure
03:32 Location of Resultant Pressure Force (Centroid of Triangle)
04:10 Potential Energy Conservation Equation
04:14 Calculating the Pressure Force (F_P)
06:07 Solving for the Resisting Force (F_R)
06:35 Key Takeaways and Summary


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