Q1. [1] § 9.1 Heights and Distances § 9.2 Summary
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is $10\sqrt{3}$ m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is
- A 30°
- B 45°
- C 60°
- D 90°
Previously asked in CBSE board exam
2025 30/6/1 Q13
Generated by claude-sonnet-4-6 · 2026-06-15 10:37 · grounding rag
Model Answer
Option A: 30°
Here, height of tree = 10 m, horizontal distance = $10\sqrt{3}$ m. $\tan\theta = \frac{10}{10\sqrt{3}} = \frac{1}{\sqrt{3}}$, so $\theta = 30°$.
Explanation
Use $\tan(\text{angle of depression}) = \frac{\text{height}}{\text{horizontal distance}}$. Since the peacock looks down, the angle of depression equals the angle whose tangent is $\frac{10}{10\sqrt{3}} = \frac{1}{\sqrt{3}}$, giving 30°. A common mistake is inverting the ratio and getting 60°—always put height in the numerator and base distance in the denominator when using tan for angle of depression from the top.
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