Question

From the top of a cliff 200 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45° respectively.what is the height of the tower?

Answer 1

let the height of the tower(DC) be h meter.
DC=BE = h meter
so , AE = AB-BE =(200-h )meter
In ∆ABC ,
AB/BC =tan 45°
200/BC= 1 (tan 45°= 1)
BC = 200 meters
since DE = BC
therefore ,
DE= 200 meter

Now ,
in ∆ AED,
AE/ED = tan 30°
(200-h)/200 = 1/√3
√3(200-h) =200
200√3- h√3 =200
h√3 = 200√3-200
h√3=200(√3-1)
so, h = 200(√3-1)/√3 meter



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Answer 2

Answer:

200(√3-1) /√3 is the answer I think soo