A man 160cm tall is at a distance of 600cm from foot of a light source situated at top of pole of height 4.1m high.Find distance between top of a man and source of light?
Let the height of man be AB = 160 cm
Let the height of pole be DC = 4.1 m = 410 cm
Let the distance between the man and pole be DC = 600 cm
DC = DE + EC
∴ 410 cm = DE + 160 cm
∴ DE = 410 cm – 160 cm
= 250 cm
In ΔAED, right angled at E, applying Pythagoras theorem,
AD2 = DE2 + AE2
∴ AD2 = (250)2 + (600)2
⇒ AD2 = 62500 + 360000
⇒ AD2 = 422500
⇒ AD = 650 cm
Thus, the distance between the top of man and source of light is 650 cm.