Question

A water tank casts a shadow $21m$ long. A tree of height $9.5m$ casts a shadow $8m$ long at the same time. The lengths of the shadows are directly proportional to their heights. Find the height of the tank in cm.

Answer 1

R.E.F image

Ans - Here we have a water tank and a tree

of height 9.5 m casting shadow at

same time

at same time both make equal inclined

angle so, by $tan\theta$ in (i) and (ii)

$tan\theta =\frac{x}{21}...\left(1\right);tan\theta =\frac{9.5}{8}=\frac{95}{80}...\left(2\right)$

by eq. (1) & (2)

$\frac{x}{21}=\frac{95}{80}\Rightarrow \frac{95}{80}\Rightarrow x=24.93$

$\Rightarrow x=24.90(appr.)$