Question

A 1.5m tall boy stands at a distance of 3m from a lamp post and casts a shadow of 4.5m on the ground.find the height of lamp post by trignometric ratios

Answer 1

Let AB be boy = 1.5m
CD be lamp = Let it be x m.
OB be shadow cast by boy = 4.5m
BD be distance between boy and lamp = 3m

Therefore
In ΔAOB,
=> tan θ = AB/OB
In ΔCOD,
=> tan θ = CD/OD = CD/(OB+BD)

∴ AB/OB = CD/(OB+BD)
=> 1.5/4.5 = CD/(4.5+3)
=> CD = 7.5/3 = 2.5m

Answer 2

Answer: Height of boy = 3/2 Shadow of boy = 9/2 therefore angle of elevation: tan Q = 1.5/4.5 = 1/3 using the value of tan Q, distance of lamp from boy = 3 let height of lamp be "x" meter greater than boy, then tan Q = x/3 substituting value of tan Q 1/3 = x/3 x = 1. therefore height of lamp = 3 + 1 = 4 meter