Question

1 meter 60cm from a projector a 50cm object is placed. How big will your shadow cast on a screen 14 meters from the projector?​

Answer 1

Given:

1 meter 60 cm from a projector a 50 cm object is placed.

To Find:

How big will your shadow cast on a screen 14 meters from the projector?​

Solution:

Distance of object from projector:

FC = 160 cm

Distance of shadow from projector:

CG = 1400 cm

Height of object is given:

AB = 50 cm

From attach figure it is clear that projector is at point C and object is represented by AB and shadow is represented by DE:

From attach figure , it is clear that:

$\mathbf{\Delta ABC \sim \Delta EDC}$    (By AAA rules)

So, we can also write:

$\mathbf{\frac{DE}{CG}=\frac{AB}{FC}}$

On putting respective value in above:

$\mathbf{\frac{DE}{1400}=\frac{50}{160}}$

On solving , we get:

DE = 437.5 cm

Means height of shadow cast on a screen 14 meters from the projector is 437.5 cm.