Question

From the top of a cliff of height h metre the angles of depression of the top and bottom of a tower-1 are observed to be 30o and 45o respectively and that of tower-2 are 45o and 60o respectively. The ratio of heights of tower-1 to tower-2 will be

Answer 1

Answer:

first tell what is the subject

Answer 2

Given :  From the top of a cliff of height h metre the angles of depression of the top and bottom of a tower-1 are observed to be 30° and 45° respectively and that of tower-2 are 45° and 60° respectively.

To Find : ratio of heights of tower-1 to tower-2

Solution:

Height of cliff =  h m

Tan 45° = Height of cliff  / Horizontal Distance of tower 1

=> 1    = h / Horizontal Distance of tower 1

=> Horizontal Distance of tower 1  = h

Tan 30°  = (Height of cliff - Height of tower 1 ) / Horizontal Distance of tower 1

=> 1/√3  = (h  - T1) / h

=> h/√3  = h - T1

=> T1 = h  - h/√3

Tan 60° = Height of cliff  / Horizontal Distance of tower 2

=> √3   = h / Horizontal Distance of tower 2

=> Horizontal Distance of tower 2  = h/ √3

Tan 45°  = ( height of cliff - Height of tower 2 ) / Horizontal Distance of tower 2

=> 1  = ( h - T2)/( h/ √3)

=> => h/√3  = h - T2

=> T2 = h  - h/√3

T1 = T2

T1 : T2 = 1 : 1

ratio of heights of tower-1 to tower-2  is 1 : 1

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