Discussion
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60º. When he moves 50 m away from the bank, he finds the angle of elevation to be 30º.
Answer: D
Fig.
Let AD be the tree of height h,
In ΔADC,
tan60º = h/CD
Or, √3 = h/CD
Or, CD = h/√3
In ΔADB,
tan30º = h/BD
Or, 1/√3 = h/BD
Or, BD = h√3
BD - CD = 50
h√3 - h/√3 = 50
(3h - h)/√3 = 50
2h = 50√3
Height of the tree,
h = 50√3/2
= 25√3 25×1.732
= 43.3 m.
Width of the river,
CD = h/√3
= 25√3/√3
= 25 m.
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