A boy standing at one bank of a river sees the top of a tree on the other bank directly opposite to the boy at an elevation of 60°. Stepping 40m back, he sees
Answers
Given : A person standing on the bank of river observes that the angle of the elevation of the top of a tree standing on the opposite bank is 60° when he moves 40m away from bank he finds the angle of elevation to be 30 degree
To Find : the height of the tree and width of the canal
Solution:
width of the canal = w m
height of the tree = h m
Tan 60° = h/w
=> √3 = h/w
=> h = w√3
Tan 30° = h/(w + 40)
=> 1/√3 = h/(w + 40)
=> h = (w + 40)/√3
w√3 = (w + 40)/√3
=> 3w = w + 40
=> 2w = 40
=> w = 20
width of the canal = 20 m
height of the tree = 20√3 m
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