Question
The angle of elevation of the top of a tree from a point A on the ground is 60βΒ . On walking 20 m away from point A, to a point B, the angle of elevation changes to 30β. Find the height of the tree.
Answer: Option A
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A
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A
In triangle ACD,
tanΞΈ=DCCA=hx
βtan60β=β3=hxΒ ..................... 1
In triangle CDB,
βtan30β=CDCB
β1β3=hx+20....................... 2
Using (1) and (2), we get
β1β3=xβ3x+20
βx+20=3x
β2x=20
βx=10
β΄h=xβ3=10β3
Thus, the height of the tree isΒ 10β3Β m.
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