Question

an electric pole , 14 meters high, casts a shadow of 10 meters. find the height of a tree that casts a shadow of 15 meters under similar conditions​

Answer 1

Answer:

$\huge\mathcal{\red{Hola!}}$

$\huge\mathfrak{\green{Answer}}$

$\huge\mathcal{\red{21 m}}$

Step-by-step explanation:

$\mathcal{\red{ *Hint- \ We \ will \ prove \ the \ triangles \ similar \ formed \ by \ the \ pole \ and \ tree}}$

$\huge\mathfrak{\red{Now,}}$

From the figure (in attachment)

In ∆ABC:

AB= 14m

BC= 10m

In ∆DEF

let DE= h m

EF = 15 m

Now,

In ∆ABC and ∆DEF

/ B = / E (each 90°)

/ C = / F ( given that both the pole and the tree casts shadow under similar condition. Therefore, the angular elevation of both are same)

$\huge\mathcal{\red{Therefore,}}$

∆ABC ~ ∆ DEF ( By AA criteria)

$= > \frac{ab}{de} = \frac{bc}{ef}$

because congruent sides of similar triangles are in equal ratio or are in proportion.

$= > \frac{14}{h} = \frac{10}{15} = 10h = 14 \times 15$

$h = \frac{210}{10} = 21m$

Hence, the height of the tree is 21m.

Other criterias of similarity are:

• SAS ( Side Angle Side) criteria of similarity

• SSS ( Side Side Side) criteria of similarity

• AAA ( Angle Angle Angle) criteria of similarity

$\huge\mathcal{\green{ All \ the \ very \ best!}}$

$\huge\mathcal{\red{@TheDynamicPrincess}}$