A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.
A flag pole 18 m high casts a shadow 9.6 m long. Find the distance of the top of the pole from the far end of the shadow.

Solution:

NCERT Exemplar Solutions Class 10 Maths Chapter 6 Ex. 6.4-16

Let MN = 18 m be the banner shaft and its shadow be LM = 9.6 m.

The distance of the highest point of the post, N from the far end, L of the shadow is LN.

In right calculated ∆LMN,

    \[LN2\text{ }=\text{ }LM2\text{ }+\text{ }MN2\text{ }[by\text{ }Pythagoras\text{ }theorem]\]

 

    \[\Rightarrow LN2\text{ }=\text{ }\left( 9.6 \right)2\text{ }+\text{ }\left( 18 \right)2\]

    \[\Rightarrow LN2\text{ }=\text{ }9.216\text{ }+\text{ }324\]

    \[\Rightarrow LN2\text{ }=\text{ }416.16\]

    \[\therefore LN\text{ }=\text{ }\surd 416.16\text{ }=\text{ }20.4\text{ }m\]

Thus, the necessary distance is 20.4 m