(Q17) A person 1.65m tall casts 1.8m shadow. At the same instance, a lamp post casts a shadow of 5.4 m. Find the height of the lamppost.

APRQCB1.8 m5.4 m h m.?1.65 m.

Solution :

In ∆ABC and ∆PQR

∠B = ∠Q = 90o.

∠C = ∠R (AC ∥ PR, all sun's rays are parallel at any instance)

∆ABC ∼ ∆PQR ( by AA similarity)

AB
PQ
 =
BC
QR
 (cpst, corresponding parts of Similar triangles)
PQ
 =

PQ =
×
= m

The height of the lamp post is m