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 `10sqrt3` m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is ______.

Options

• 30°

• 45°

• 60°

• 90°

Answer 1

A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is `10sqrt3` m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is 30°.

Explanation:

Given:

• Height of tree = 10 m
• Distance of snake from the base of tree = `10sqrt3` m.
• We assume a right-angled triangle where:
  • The height of the tree (10 m) acts as the opposite side.
  • The distance of the snake from the base (10√3 m) acts as the adjacent side.
  • The angle of depression is θ (formed between the line of sight from the peacock’s eye to the snake and the horizontal).

Using tan function:

tan θ = `("opposite")/("adjacent")`

tan θ = `(10)/(10sqrt3)`

tan θ = `1/sqrt3`

tan30° = `1/sqrt3`

θ = 30°