NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.4

Question 7

We can imagine the situation as a right-angled triangle:

• The vertical flag pole is the height = \(18\,\text{m}\).
• The shadow on the ground is the base = \(9.6\,\text{m}\).
• The slant distance from the top of the pole to the end of the shadow is the hypotenuse (the side we need to find).

By the Pythagoras theorem, in a right triangle:

\[ \text{Hypotenuse}^2 = \text{Base}^2 + \text{Height}^2 \]

Substitute the values:

\[ \text{Hypotenuse}^2 = (9.6)^2 + (18)^2 \]

\[ = 92.16 + 324 \]

\[ = 416.16 \]

Now take the square root:

\[ \text{Hypotenuse} = \sqrt{416.16} \]

\[ = 20.4\,\text{m} \]

So, the distance from the top of the flag pole to the far end of the shadow is 20.4 metres.