Question

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







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Answer 1

Answer:

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Answer 2

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

Hope it helped

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