Question

33. From the top of a building 20 m high, the angle of elevation of the top of a monument
is 45° and the angle of depression of its foot is 15º. Find the height of the monument.
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Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

Answer:

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