Question

A pit slope has the following information: Number of benches = 5, Height of each bench = 8 m, Bench slope angle = 70° If the width of one bench is 24 m and that of other four benches is 10 m each, the overall pit slope angle, in degree, is ________ (rounded off to 2 decimal places).

Hint:

To estimate pit slope angle: \( \tan \theta = \frac{{Total Height}}{{Total Width}} \), or use vector geometry for accurate slope modeling.

Answer 1

Step 1: Calculate the total horizontal distance (width) of the pit. \[ {Total width} = 24 \, {m} + (4 \times 10 \, {m}) = 24 \, {m} + 40 \, {m} = 64 \, {m} \] Step 2: Calculate the total height of the pit. \[ {Total height} = 5 \times 8 \, {m} = 40 \, {m} \] Step 3: Calculate the overall slope angle. \[ \tan(\theta) = \frac{{Total height}}{{Total width}} = \frac{40 \, {m}}{64 \, {m}} = 0.625 \] \[ \theta = \tan^{-1}(0.625) \approx 32.47^\circ \] Thus, the overall pit slope angle is approximately \( \boxed{32.47^\circ} \).