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+----- Thread: TIER 7 — CHALLENGE 003 — The Mountain Shadow Geometry (/showthread.php?tid=161)
TIER 7 — CHALLENGE 003 — The Mountain Shadow Geometry - Leejohnston - 11-14-2025
[border]TIER 7 — Advanced Reasoning[/border]
Tier 7 — Challenge 003 — The Mountain Shadow Geometry
At sunrise, a tall mountain casts a shadow across a valley.
• Mountain height: **2,480 m**
• Angle of sunlight above the horizon: **7.5°**
• The mountain peak is tilted **3° forward** due to local terrain slope
Questions:
1. What is the length of the shadow on flat ground?
(Adjust the effective height using the 3° tilt.)
2. If the valley floor rises by **100 m** over the shadow distance,
how does this affect the final shadow length?
3. Explain the geometry clearly — this is a Tier 7 thinking challenge.
? Submit Your Attempt
Thread title:
Tier 7 Attempt — YourUsername — Challenge 003