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 PLZZ ANSWER FAST
Answers
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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