Question

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. $60^\circ$
• B. $45^\circ$
• C. $30^\circ$
• D. $90^\circ$

Hint:

Use tan = height/base to find angle of elevation or depression.

Answer 1

The Correct Option is C

Given:
- Height of the tree = 10 m
- Distance of the snake from the base of the tree = \(10\sqrt{3}\) m

Step 1: Understand the triangle formed
Let the top of the tree be point \(P\), the base of the tree be point \(B\), and the position of the snake on the ground be point \(S\).
Then triangle \(PBS\) is a right-angled triangle with:
- Vertical side \(PB = 10\) m (height)
- Base \(BS = 10\sqrt{3}\) m (horizontal distance)
- \(\angle PSB\) is the angle of depression (same as angle at base in triangle)

Step 2: Use tangent function
\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{PB}{BS} = \frac{10}{10\sqrt{3}} = \frac{1}{\sqrt{3}} \]
Step 3: Use standard trigonometric value
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \Rightarrow \theta = 30^\circ \]
Final Answer:
The angle of depression is \(30^\circ\).