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The angle of elevation of the top of a vertical tower from a point A, due east of it is 45°. The angle of elevation of the top of the same tower from a point B, due south of A is 30°. If the distance between A and B is 54√2 m , then the height of the tower (in metres), is :

 

a) 36/√3          b) 54

c) 54/√3          d) 108

 

Asked by Ranjeetgupta26068 16th May 2019, 12:11 AM
Answered by Expert
Answer:
AB space equals 54 square root of 2
also space using space pythgoras space we space get
straight y squared equals straight x squared plus open parentheses 54 square root of 2 close parentheses squared ____ open parentheses 1 close parentheses

angle DAO space equals space 45 degree
tan space 45 space equals space straight h over straight x
straight h equals x____ open parentheses 2 close parentheses

angle DBO space equals space 30 degree
tan space 30 space equals space straight h over straight y
square root of 3 straight h equals y____ open parentheses 3 close parentheses

sub space open parentheses 2 close parentheses & open parentheses 3 close parentheses space in space open parentheses 1 close parentheses
we space get space
open parentheses square root of 3 straight h close parentheses squared equals open parentheses straight h close parentheses squared plus open parentheses 54 square root of 2 close parentheses squared
straight h equals space 54 straight m
Answered by Expert 17th May 2019, 9:45 AM
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