SME
Physical Geology · Problem type
Thickness of a dipping bed
Use this for “A sandstone dipping 30° crops out 120 m wide on flat ground, measured square to strike. How thick is it?”
Diagram
sin δ = t/w = 60/120 ≈ 0.5
cos δ = b/w = 103.92/120 ≈ 0.866
tan δ = t/b = 60/103.92 ≈ 0.5774
This is an example. Type your own values to start a new problem.
t (m)
=
w (m)
×
sin(
δ
°)
Formulas
t
=
w
×
sin(
δ
°)
60 = 120 × sin(30°)
Assumptions
•
The ground is flat, and the width is measured square to strike, from the bed’s base to its top.
•
True thickness is measured square to the bedding, so it is never more than the outcrop width.
•
A steep bed crops out nearly as wide as it is thick; a gently dipping one far wider.
Step-by-step
WE KNOW
w = 120 m, δ = 30°
FIND
true thickness (t)
Step 1 · Find true thickness (t)
Use t = w × sin(δ°)
The width runs along the ground as the hypotenuse; the thickness is the side opposite the dip.
t
=
120
×
sin(30°)
t
=
120
×
0.5
t
=
60
m
Check
Put the numbers back in. Both sides should match.
60 = 120 × sin(30°) ✓
Topic check
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