A 16 m tall girl stands at a distance of 32 m from a la

SOLUTION

 

Let AB be the tower of height h m.

Suppose CD be the height of the girl and DE be the length of shadow of the girl.

Given, CD = 1.6 m, AD = 3.2 cm and DE = 4.8 m.

In ΔCDE,

$tanE=\frac{CD}{DE}$

$tanE=\frac{1.6}{4.8}=\frac{1}{3}$ ---(1)

In triangle BAE,

$tanE=\frac{AB}{AE}$

$\frac{1}{3}=\frac{h}{3.2+4.8}$

$\frac{1}{3}=\frac{h}{8}$

$h=\frac{8}{3}$

Length is $\frac{8}{3}m$.

Method 2:

In ΔCDE and ΔBAE,

∠CED = ∠BEA  (Common)

∠CDE = ∠BAE  (90º)

∴ ΔCDE ∼ ΔBAE  (AA similarity criterion)

$\frac{CD}{AB}=\frac{CE}{BE}=\frac{DE}{AE}$

$\frac{1.6}{AB}=\frac{4.8}{3.2+4.8}$

$\frac{1.6}{AB}=\frac{4.8}{8}$

$AB=\frac{8}{3}$

Thus, the length of the lamp post is $\frac{8}{3}m$