Q. 43

There are two temples, one on each bank of a river, just opposite to each other. One temple is 50 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are 30° and 60° respectively. Find the width of the river and the height of the other temple.

Answer :

In fig let the height of the other temple is h (m.) and distance between two temple is x (m.)


In ∆ABC


tan 60° =


tan 60° =


√3 =


x =


x = (1)


In ∆AED


tan 30° =


=


X = h√3 (2)


From eqn. (1) and eqn. (2) we get,


√3h =



h = = 16.67m


On substituting the value of ‘h’ in eqn (2)


X = 28.87m


Therefore height of the temple is 50-16.67 = 33.33m


And the distance between the two temples is 28.87m


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