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True thickness from apparent thickness 210 m

Short answer

True thickness equals vertical thickness times cosine of dip: 210 m × cos(36°) = 169.9 m.

Three bore holes were drilled to find out a stable place for dam foundation of a hydroelectric project. The apparent thickness of quartzite was found as 210 m. The attitude of the quartzite bed was 220°/36° NE. Calculate the true thickness of bedrock.

Principle: in a vertical borehole the thickness measured is the vertical (apparent) thickness tvt_v. The true thickness (perpendicular to the bedding) is smaller for a dipping bed:

t=tvcos⁡δt = t_v\cos\delta

Given

tv=210t_v = 210 m, dip δ=36∘\delta = 36^\circ (attitude 220°/36° NE).

Calculation

t=210cos⁡36∘=210×0.8090=169.89 m\begin{aligned} t &= 210\cos 36^\circ \\ &= 210 \times 0.8090 \\ &= 169.89\ \text{m} \end{aligned}
        borehole
          |
     _____|______  top of bed
    |     | tv   /
    |     |    /  t (true)
    |_____|__/__  bottom of bed
          |/ dip 36 deg

Answer: true thickness of the quartzite = 169.9 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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