Question

a girl 1 m tall is standing 6m away from the base of a lamp post . if the lamp is 4 m high then find the length of her shadow​

Answer 1

Answer:

Step-by-step explanation:

Using trigonometric ratios.

     Let AB be the height of lamp post.

     Now, in right △CDE,

⇒tanθ=  

DC

ED

​  

=  

4.8

1.6

​  

=  

3

1

​  

⟶(1)

In , △ACB,

⇒tanθ=  

BC

AB

​  

=  

3.2+4.8

AB

​  

=  

8

AB

​  

⟶(2)

From (1)&(2) we get

⇒  

3

1

​  

=  

8

AB

​  

 

⇒AB=  

3

8

​  

=2.67m

∴ Height of the lamp post =2.67m

(ii) Using similar triangles :

       In △CDE&△CBA

i)∠CDE=∠CBA=90°

ii)∠DCE=∠BCA  (Common)

∴△CDE∼△CBA  ( By AA similarities )

Hence,  

AB

DE

​  

=  

BC

CD

​  

 

⇒AB=  

CD

DE×BC

​  

 

            =  

4.8

1.6×8

​  

 

            =  

3

8

​  

 

            =2.67m

∴ Height of lamp post =2.67m.

Hence, the answer is 2.67.