Question

A tower casts a shadow 90 m long and at the same time another tower casts a shadow of 120 m on the ground. If the height of the second tower is 80 m, then the height of the first tower is ???? ​

Answer 1

$\bold{\underline{\underline{Answer:}}}$

Height of the first tower = 60 m

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

• A tower casts a shadow 90 m long
• Another tower casts a shadow of 120 m on the ground
• Height of the second tower is 80 m

To find :

• Height of the first tower

Solution :

AB = x = Height of the first tower

AC = 90 m = Shadow casted by first tower

PC = 120 m = Shadow casted by second tower

PQ = 80 m = Height of the second tower

In Δ ABC and Δ PQC,

$\bold{\frac{AB}{PQ}}$ = $\bold{\frac{BC}{QC}}$ = $\bold{\frac{AC}{PC}}$

In the above pairs of corresponding sides of Δ ABC and Δ PQC, we don't require the pair of $\bold{\frac{BC}{QC}}$.

•°• Required pairs to solve the question,

$\implies$ $\bold{\frac{AB}{PQ}}$ = $\bold{\frac{AC}{PC}}$

Substitute the appropriate values of the sides,

$\implies$ $\bold{\frac{x}{80}}$ = $\bold{\frac{90}{120}}$

Cross multiplying,

$\implies$ $\bold{120\times\:x\:=\:90\times\:80}$

$\implies$ $\bold{x\:=\:{\frac{7200}{120}}}$

$\implies$ $\bold{x\:=\:{\frac{720}{12}}}$

$\implies$ $\bold{x\:=\:60}$

•°• Height of the first tower = x = 60 m

Answer 2

ANSWER:-

Given:

•A tower casts a shadow 90m long &

•Another casts a shadow of 120m on the ground.

•Height of the second tower is 80m.

To find:

The height of the first tower.

Solution:

•Let AB & CD be a tower & a pole respectively.

•Let the shadow of BE & DF be the shadow of AB & CD respectively.

At the same time, the light rays from the sun will fall on the ground & the pole at the same angle.

Therefore,

angle DCF = angle BAE

&

angle DFC = angle BEA

angle CDF= angle ABE

[tower & pole are vertical to the ground]

So,

∆ABE ∼ ∆CDF [AAA similarity criterion]

$= > \frac{AB}{CD} = \frac{BE}{DF} \\ \\ = > \frac{AB}{80} = \frac{120}{90} \\ [cross \: multiplication] \\ \\ = > AB \times 90 = 120 \times 80 \\ \\ = > AB = \frac{120 \times 80}{90} \\ \\ = > AB = 106.66m$

Thus,

The height of the first tower is 106.66m.

Hope it helps ☺️