Q19 of 47 Page 1

The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45 � and 60 � respectively. Find the height of the tower and the horizontal distance between the tower and the building.

From the condition given in the question the figure can be drawn as follows:


Let us assume AE be the building and CD be the tower


Let the height of the tower be h m


And horizontal distance between tower and building be x m


It is given in the question that,


BD = AE = 50 m


∴ BC = CD – BD


= (h – 50) m


Now in right triangle ABC, we have:




∴ x = h – 50 (i)


Also, in right triangle CDE, we have




Now putting the value of x from (i) we get:





∴



= 25 × 4.73


= 118.25


Now, putting the value of h in (i) we get:


x = h – 50


= 118.25 – 50


= 68.25 m


Hence, height of the tower is 118.25 m and the horizontal distance between tower and building is 68.25 m


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