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Question

A man 2 m tall, standing on top of a 25 m building observe the angle of depression of the top and bottom of the next building to be 30 and 60 respectively. The height of the next building is ____ m.


Solution

The diagram can be visualised as shown in the figure.

Let the height of next building be h.

In ΔADE, tan30 = (27h)DE) 

   1(3)(27h)DE       ----------------------------- I

In ΔABC, tan60= 27BC       

    (3)27BC                           ------------------------------II

DE = BC, so dividing I by II , we get

3 =  27(27h)                 h =18m

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