Q12 of 25 Page 9

From the top of a building 15 m high the angle of elevation of the top of a tower is found to be 30° . From the bottom of the same building, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower and the distance between the tower and building.

To Find:


The distance between tower and building.


Formula Used:



Explanation:



Let the distance between tower and building = (m)


In ∆ABC,


tan 60° =


√3 =


=


√3 = h+15


h = √3-15


In ∆ABE,


tan 30° =



)


Substituting value of x in eqn.(1)



h = 3h-15 ⇒ 2h = 15


h = ⇒ 7.5 m.


Height of tower = 15+7.5 ⇒ 22.5 m.


⇒ 12.99 m.


Therefore distance between tower and building is 12.99 m.


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