Question

The angle of elevation of top of the cliff from a point 300 m from its foot is 600. Then the height of the cliff is

• A. \(300\sqrt{3}\)
• B. \(200\sqrt{3}\)
• C. \(\frac{300}{\sqrt{3}}\)
• D. \(\frac{200}{\sqrt{3}}\)

Answer 1

The Correct Option is A

To solve the problem, we need to find the height of the cliff given the angle of elevation and the horizontal distance from the cliff.

1. Understanding the Triangle:
This forms a right-angled triangle where:
- The height of the cliff is the opposite side
- The distance from the foot of the cliff is the adjacent side = 300 m
- The angle of elevation = $60^\circ$

2. Using Trigonometric Ratio:
We use the tangent function since it relates the opposite and adjacent sides:

$ \tan \theta = \frac{\text{opposite}}{\text{adjacent}} $

$ \tan 60^\circ = \frac{\text{height}}{300} $

3. Substituting the Value of $\tan 60^\circ$:

$ \sqrt{3} = \frac{\text{height}}{300} $

$ \text{height} = 300 \times \sqrt{3} $

Final Answer:
The height of the cliff is $ 300\sqrt{3} \, \text{m} $.