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From a point on the ground 40m away from the foot of the tower ,the angle of elevation of the top of the tower is 30. The angle of elevation of the top of the water tank (on the top of the tower) is 45, find height of the tower and the depth of the tank

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We have given a question from trigonometry of height and distance in which we have to find the height of the tower and the depth of the tank if from a point on the ground 40m away from the foot of the tower ,the angle of elevation of the top of the tower is 30. The angle of elevation of the top of the water tank (on the top of the tower) is 45.

Book RS Aggarwal, Class 10, chapter 14, question no 6.

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1. Let the height of the tower beÂ h. Let the height of the tank beÂ x. Hence total length of the structureÂ =h+x.

Now applying trigonometric ratios, we get
tan45Â°=(h+x)/40m =1â€‹

Hence
h+x=40mÂ …(i)

Also
tan30Â°=h/40â€‹=1/âˆš3â€‹

Hence
h=40âˆš3/3â€‹â€‹
=23.09m

Now
x=40âˆ’â€‹40/âˆš3â€‹

=40(âˆš3â€‹âˆ’1â€‹)/âˆš3

=16.905m

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