Question

Q4. A girl, 1.5 m tall stands in front of a lamp post and casts a shadow 4 m long on the ground. If she is standing at a distance 8 m from the lamp post, find the height of the lamp post.

Answer 1

Answer:

4.5 m

Step-by-step explanation:

Refer the diagram of the image attached.

Suppose, AB be the lamp post, EC be the girl and CD be the shadow and ∠ADB = θ

Given, BC = 8 m,  CD = 4 m,  EC = 1.5 m

In triangle CDE,

tan θ = CE / CD = 1.5 / 4 = 3 / 8 m   [Multiplying numerator and denominator by 2]

In triangle ABD,

tan θ = AB / BD = x / (4 + 8) = x / 12  [Let x be height of lamp post]

∵ Both triangles CDE & ABD are on same base and also subtend same angle at D i.e. θ,

⇒ tan θ of CDE = tan θ of ABD

⇒ 3 / 8 = x / 12

⇒ x = 12 * 3 / 8 = 4.5 m