NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 8: Introduction to Trignometry and Its Applications - Exercise 8.3

Question 8

Step 1: Draw a right triangle to represent the situation.

• The vertical pole is the opposite side of the right triangle.
• The shadow on the ground is the adjacent side.
• The angle of elevation of the Sun is the angle \(\theta\) formed between the line from the top of the pole to the tip of the shadow and the ground.

Step 2: Write down the given information.

• Height of pole = \(h\) metres
• Length of shadow = \(\sqrt{3}\,h\) metres

Step 3: Recall the trigonometric ratio for tangent:

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

Step 4: Substitute the values.

\[ \tan(\theta) = \dfrac{h}{\sqrt{3}h} \]

Step 5: Simplify.

\[ \tan(\theta) = \dfrac{1}{\sqrt{3}} \]

Step 6: Recall the standard trigonometric value.

\[ \tan(30^\circ) = \dfrac{1}{\sqrt{3}} \]

Step 7: Therefore, \(\theta = 30^\circ\).