MCQ
A vertical stick $20\ cm$ long casts a shadow $15\ cm$ long. At the same time, a tower casts a shadow $30m$ long. The height of the tower is :
- ✓$40m$
- B$20m$
- C$30m$
- D$15m$
✓
Answer
Correct option: A.
$40m$
Let the height of the vertical stick be $AB = 20\ cm,$ the length of the shadow of the stick be $BC = 15\ cm$ and angle of elevation $\theta$
At the same time the height of the tower be $h$ meters and the shadow of the tower $= QR = 30\ cm$ and the angle of elevation.
$\angle\text{PRQ}=\theta$
Now, in triangle $\text{ABC},$
$\tan\theta=\frac{\text{AB}}{\text{BC}}$
$\Rightarrow\tan\theta=\frac{20}{15}=\frac{4}{3}.....(\text{i})$
Again in triangle $\text{PQR},$
$\tan\theta=\frac{\text{PR}}{\text{QR}}$
$\Rightarrow\frac{4}{3}=\frac{\text{h}}{30}\ [$From eq. $(i)]$
$\Rightarrow\text{h}=\frac{30\times4}{3}=40\text{ meters}$
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