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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.

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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

DE=3(27h) ----------------(i)

In ΔABC, tan60= 27BC

(3) = 27BC) -

BC=273------------------(ii)

DE = BC, Hence equating (i) and (ii) , we have

3(27h) = 273

3(27h)=27

813h=27

3h=54

h = 18 m


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