--- title: "Calculating apparent dip from true dip" subject: "Engineering Geology I" chapter: 5 key: "semester_3/engineering_geology_i:calculating-apparent-dip-from-true" source: https://www.bctengineer.com/q/semester_3/engineering_geology_i/calculating-apparent-dip-from-true site: BCT Engineering --- # Calculating apparent dip from true dip Engineering Geology I · Chapter 5: Structural Geology - Asked in: 2073 Shrawan, 4 marks - Video: [Structural Geology Lesson 2: Apparent Dip](https://www.youtube.com/watch?v=-TPje1Ef-x4) — Blake Splitter - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/engineering_geology_i/calculating-apparent-dip-from-true - Whole chapter: https://www.bctengineer.com/md/semester_3/engineering_geology_i/chapter-5 ## Question How do you calculate the apparent dip amount when the true dip amount is measured? ## Short answer Apparent dip is given by tan δ_a = tan δ × sin α, where δ is true dip and α is the horizontal angle between the strike and the section direction. For true dip 30° and α=45°, tan δ_a = 0.5774 × 0.7071 = 0.4082, so apparent dip = 22.2°. ## Answer **Apparent dip** is the inclination of a bed measured in a vertical section that is not perpendicular to the strike. It is always smaller than the true dip. #### Formula Let $\delta$ be the true dip, and $\alpha$ be the horizontal angle between the strike line and the direction (section line) in which the apparent dip $\delta_a$ is wanted. $$ \tan \delta_a = \tan \delta \times \sin \alpha $$ #### Derivation ```text strike A --------------- B \ | / \ | h(depth) \ | C ------- D true dip: CD is perpendicular to strike ``` Take a point on the strike line at height 0 and go a horizontal distance $x$ in the apparent-dip direction. The bed falls by $h$. - Along the true-dip direction (perpendicular to strike): the horizontal distance is $d = x\sin\alpha$ for the same fall $h$, so $\tan\delta = h/d$. - Along the apparent-dip direction: $\tan\delta_a = h/x$. - Hence $\tan\delta_a = \tan\delta \cdot d/x = \tan\delta \sin\alpha$. #### Procedure 1. Measure strike and true dip from the compass. 2. Measure the bearing of the section line and find $\alpha$ = difference between the two bearings (use the acute angle). 3. Apply the formula and take the inverse tangent. #### Example True dip = 30°, section line makes $\alpha = 45°$ with the strike. $$ \tan \delta_a = \tan 30° \times \sin 45° = 0.5774 \times 0.7071 = 0.4082 \Rightarrow \delta_a = 22.2° $$ **Check**: for $\alpha = 90°$, $\delta_a = \delta$ (true dip); for $\alpha = 0°$ (along the strike), $\delta_a = 0°$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which formula relates apparent dip to true dip? A. tan(apparent dip) = tan(true dip) x cos(alpha) B. sin(apparent dip) = tan(true dip) x sin(alpha) C. tan(apparent dip) = tan(true dip) x sin(alpha) D. apparent dip = true dip x sin(alpha) Answer: C. Alpha is the angle between strike and the section line. (Key point: Formula) 2. What is alpha in the formula? A. The horizontal angle between the strike line and the section direction B. The angle between dip direction and north C. The true dip itself D. The angle of the slope surface Answer: A. Apparent dip depends on how far the section line is from the strike. (Key point: Meaning of alpha) 3. What is the apparent dip along the strike? A. Equal to the true dip B. 0° C. 90° D. Half the true dip Answer: B. alpha = 0 gives sin 0 = 0, so tan(apparent) = 0. (Key point: Limiting cases) 4. True dip 30° and alpha 45° give an apparent dip of about A. 30° B. 45° C. 15° D. 22.2° Answer: D. tan = 0.5774 x 0.7071 = 0.4082, so apparent dip = 22.2°. (Key point: Numerical example) ## Close variants set in other exams - [Strike-dip relationship and apparent dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrikedip-relationship-and-apparent-dip) — Engineering Geology I, chapter 5, asked 2× ## Related in Engineering Geology I - [True dip versus apparent dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Atrue-dip-versus-apparent-dip) — Engineering Geology I, chapter 5, asked 2× - [Fold classification, strike, true and apparent dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Afold-classification-strike-true-and) — Engineering Geology I, chapter 5 - [Apparent dip in cross-section drawing](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aapparent-dip-in-crosssection-drawing) — Engineering Geology I, chapter 5 - [Dip amount, strike; fold identification criteria](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Adip-amount-strike-fold-identification) — Engineering Geology I, chapter 5 - [Primary and secondary structures; strike and dip](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aprimary-and-secondary-structures-strike) — Engineering Geology I, chapter 5, asked 2× - [Strike of limestone bed, dip N40°W, 64°](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Astrike-of-limestone-bed-dip) — Engineering Geology I, chapter 5 ## Related in other subjects - [True dip from two apparent dips](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Atrue-dip-from-apparent-dips) — Engineering Geology II, chapter 6 - [Reserve: limestone dip 30, apparent 20 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-limestone-dip-30) — Engineering Geology II, chapter 7 - [True thickness from apparent thickness 210 m](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Abh-quartzite-thickness-210-attitude) — Engineering Geology II, chapter 6 - [Reserve: quartzite apparent dips 1:9 and 1:12, 2.7 x 3.1 km](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Areserve-quartzite-apparent-dips-terrain) — Engineering Geology II, chapter 7, asked 2×