Q10 of 12 Page 203

From a window 15m high above the ground in a street, the angles of elevation and depression of the top and foot of another house on the opposite side of the street are 30° and 45° respectively. Show that the height of the opposite house is 23.66m. (take √3 = 1.732).

The figure is given below:



From fig;


AB = 15m


So, AB = CD = 15m


In triangle ABC,


∠ ACB = 45°


tan 45° = 1



⇒ AB = CB


So, CB = 15m


Also, CB = AD = 15m


Now, in triangle EAD,


∠ EAD = 30°





ED = 8.66m


So, height of building = ED + DC = 8.66 + 15


= 23.66m


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