Question

What is the angle of elevation of the Sun, if the length of the shadow of a tower is \(\frac{1}{\sqrt3}\) the height of the tower? 

• A. 30°
• B. 45°
• C. 60°
• D. None of these

Answer 1

The Correct Option is C

Step 1: Represent the problem using trigonometry.

Let the height of the tower be \( h \), and let the length of the shadow be \( s \). From the problem, we know:

\[ s = \frac{1}{\sqrt{3}} h. \]

The angle of elevation of the Sun is the angle \( \theta \) between the ground and the line from the top of the tower to the tip of the shadow. Using the tangent function:

\[ \tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{\text{height of the tower}}{\text{length of the shadow}} = \frac{h}{s}. \]

Step 2: Substitute \( s = \frac{1}{\sqrt{3}} h \).

\[ \tan\theta = \frac{h}{\frac{1}{\sqrt{3}} h} = \sqrt{3}. \]

Step 3: Determine the angle \( \theta \).

The value of \( \tan\theta = \sqrt{3} \) corresponds to \( \theta = 60^\circ \).

Final Answer: The angle of elevation of the Sun is \( \mathbf{60^\circ} \), which corresponds to option \( \mathbf{(3)} \).