Question

an adult and a minor boy standing on the ground are two metres the height of the adult is 4times the height of minor boy find mid point and line segment

Answer 1

Join A and E to D ,

 

Let the height of the minor boy = DE = h m

 

the height of the Adult = AB = 4h m

 

Distance between them = BC = 2m

 

BC = CD = 1 m

 

i ) In triangle ABC ,

 

Angle ACB = x

 

< ABC = 90

 

Tan x = AB / BC

 

Tan x = 4h /1 ---------( 1 )

 

ii ) in triangle ECD,

 

Angle ECD = 90 - x ( since completary angles )

 

< EDC = 90

 

Tan ( 90 - x ) = ED / CD

 

Cot x = h / 1 ------( 2 )

 

Multiply ( 1 ) and ( 2 ), we get,

 

Tan x Cot x = 4h × h

 

1 = 4h^2

 

1/4 = h^2

 

h^2 = 1/4

 

h = 1/2 m

 

Therefore,

 

Height of the boy = h = 1/2 = 0.5 m

 

Height of the adult = 4h = 4 × 0,5 = 2 m

 

Hope This Helps :)