Question

The angle of elevation of the top of a vertical tower
from a point A on the ground is 45º. The angle of
elevation of the top of the same tower from a point B
on the same side of A is 30°. If the distance between
A and B is 54√2 m, then the height of the tower is__.




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Answer 1

Answer:

height of the tower is 27√2(√3+1) m

Explanation:

from the figure,

it is clear that ,

h cot 30°-h cot 45°=54√2

=>h(√3-1)=54√2

=>h=54√2/(√3-1)

=>h=27√2(√3+1). (answer)

Answer 2

Given :-

Angle of elevationof top of point A and B = 45° and 30° Respectively.

To Find :-

Height Of tower 'H'.

Answer :-

Height(H) = 27√2(3-√3)

Step By step explaination :-

Let 'H' be the height of The tower between A and B,

And 'h' be the height between point B And C where C is the ground where tower is situated.

Using Trigonometry,

=> tan45° = AC/AD

=> 1= 54√2+h/CD----(1)

and,

=> tan 30° = h/CD

=> 1/√3= h/CD

CD=h√3

so,

=> 1= (54√2+h)/h√3----From(1)

=> h√3=(54√2+h)/h√3

=>h√3=54√2+h

=>h(√3-1)=54√2

So value of small 'h' =54√2/(√3-1)

From (1) Using to find CD.

=> 1= (54√2+h)/CD

=> CD= 54√2+h

So,

=> 1/√3= h/CD

=> CD = h√3h

again,

=>h√3=54√2+h

=>h(√3-1)= 54√2

=> h=54√2/(√3-1)

=>Rationalising Directly,

=> H= 27√2(3-√3)

Ans.