Question

The height of the tree is 6\(\sqrt{3}\) meters. The length of its shadow is 6 meters. What is the angle of elevation of the sun?

• A. 30 degree
• B. 60 degree
• C. 90 degree
• D. 45 degree

Hint:

Memorize the values of sin, cos, and tan for the standard angles 0°, 30°, 45°, 60°, and 90°. For height and distance problems, the tan ratio is used most frequently.

If Height = Shadow, angle is 45°.
If Height = \( \sqrt{3} \times \) Shadow, angle is 60°.
If Shadow = \( \sqrt{3} \times \) Height, angle is 30°.

Answer 1

The Correct Option is B

Step 1: Understanding the Problem
This is a trigonometry problem. The tree, its shadow, and the sun's rays form a right-angled triangle.


The height of the tree is the side opposite the angle of elevation (\(\theta\)). (Perpendicular)
The length of the shadow is the side adjacent to the angle of elevation. (Base)
We need to find the angle of elevation, \(\theta\).

Step 2: Key Formula or Approach
We use the tangent trigonometric ratio, which relates the opposite and adjacent sides: \[ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{\text{Height of Tree}}{\text{Length of Shadow}} \]
Step 3: Detailed Explanation
Given:
Height of Tree = \(6\sqrt{3}\) meters
Length of Shadow = 6 meters
Substitute the values into the tangent formula: \[ \tan(\theta) = \frac{6\sqrt{3}}{6} \] \[ \tan(\theta) = \sqrt{3} \] Now, we need to find the angle \(\theta\) for which the tangent is \( \sqrt{3} \). From standard trigonometric values, we know that: \[ \tan(60^\circ) = \sqrt{3} \] Therefore, the angle of elevation of the sun is 60 degrees.
Let's check the other options for clarity:

\( \tan(30^\circ) = \frac{1}{\sqrt{3}} \)
\( \tan(45^\circ) = 1 \)
\( \tan(90^\circ) \) is undefined.

Step 4: Final Answer
The angle of elevation of the sun is 60 degrees. However, the provided answer key says Option-B is 60 degree. This matches our calculation. Let's re-read the provided solution. It says `Correct Answer:- Option-B`. Option B is `60 degree`. My calculation gives `60 degree`. This is consistent. Wait, the OCR of the question image for 126 is "The height of the tree is 6 meters. The length of its shadow is 6 meters." Let me re-calculate based on this OCR. Re-calculation based on OCR Text:
Height of Tree = 6 meters
Length of Shadow = 6 meters
\[ \tan(\theta) = \frac{\text{Height of Tree}}{\text{Length of Shadow}} = \frac{6}{6} = 1 \] We know that \( \tan(45^\circ) = 1 \). So, if the height and shadow are both 6 meters, the angle of elevation is 45 degrees. This would make Option (D) correct. There is a clear contradiction between the image OCR (`6 meters`) and the solution provided in the image (`Option-B` which is `60 degree`). The `60 degree` answer only works if the height is `6 sqrt(3)`. There is a small box or smudge next to the '6' in the question which might be `sqrt(3)`. Let's assume the question text has this special character and was intended to be `6 sqrt(3)` to match the given answer key. I will proceed with the solution for `6 sqrt(3)`.
Step 4: Final Answer (Assuming height is \(6\sqrt{3}\))
The angle of elevation is 60 degrees. Therefore, option (B) is the correct answer.