NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications - Exercise 8.1

Question 15

Step 1: Draw a right-angled triangle.

- The pole is the vertical side (opposite side) = \(6\,\text{m}\).

- The shadow is the horizontal side (adjacent side) = \(2\sqrt{3}\,\text{m}\).

- The angle of elevation of the Sun is \(\theta\) (the angle between the sunlight and the ground).

Step 2: Use the definition of tangent.

\( \tan\theta = \dfrac{\text{opposite side}}{\text{adjacent side}} \)

Here, opposite = height of pole = \(6\,\text{m}\), adjacent = shadow length = \(2\sqrt{3}\,\text{m}\).

Step 3: Substitute the values.

\( \tan\theta = \dfrac{6}{2\sqrt{3}} \)

Step 4: Simplify the fraction.

\( \dfrac{6}{2\sqrt{3}} = \dfrac{3}{\sqrt{3}} = \sqrt{3} \)

Step 5: Recall the trigonometric ratio.

\( \tan 60^\circ = \sqrt{3} \)

Step 6: Therefore, \( \theta = 60^\circ \).

Final Answer: The Sun’s elevation is \(60^\circ\).