Question

From the top of a building 20m high, the angle of elevation of the top of a monument is 45degree and the angle of depression of its foot is 15 degree. Find the height of the monument.

Answer 1

let AB be the building (with A at top) and CD be the monument (with C at top)
let AE║BD, AE = BD and AB = ED

In ΔAEC,
           tan 45° = CE/ AE
        ⇒ CE = AE             (tan 45° = 1) ................................ 1

alternate interior angles are equal
          ⇒ EAD = BDA = 45°

In ΔABD
          tan 45° = AB/ BD 
                 ⇒ AB = BD          (tan 45° = 1) ................................ 2

Since AE = BD
              AB = CE                 (from 1 and 2)

thus the height of monument = CE + ED = CD = 20 + 20
                                                    = 40 m

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Answer 2

Step-by-step explanation:

From the top of a building of 20m high the angle of elevation of the top of a monument is 45⁰ and the angle of depression of the foot of the monument is 30⁰. Find the height of the monument in nearest metre.