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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

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
 

Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
let the top of the tower be called T, and base of tower be S.
then ST=SA coz of 45 degree.
also, ST/SB= tan30= 1/root3
also, by pyth theorem,
SB^2= AB^2+SA^2
we are given AB= 54√2 and SB= STroot3= SAroot3
so 2SA^2= 54^2*2
or SA= 54= ST
so option B 54 m is correct

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