Question

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground. Find the height of the lamp-post by using (i) trigonometric ratios (ii) property of similar triangles.

Answer 1

(i) trigonometric ratios   8/3 m

(ii) property of similar triangles  8/3 m

Given,

A 1.6 m tall girl stands at a distance of 3.2 m from a lamp-post and casts a shadow of 4.8 m on the ground.

Consider the figure while going through the following steps:

From figure it's clear that,

Δ ABC ~ Δ BDE

AC / BC = ED / BE

AC / (BE + EC) = ED / BE

h / (4.8 + 3.2) = 1.6 / 4.8

h / 8 = 1 / 3

h = 8 / 3  ..............(i)

In Δ ADE,

tan ∅ = DE / BE

tan ∅ = 1.6 / 4.8 = 1 / 3

In Δ ABC

tan ∅ = AC / BC

1 / 3 = h /  (4.8 + 3.2)

1 / 3 = h / 8

h = 8 / 3 ............(ii)

Answer 2

Answer:

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