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A person standing on the bank of the river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60∘.When he was 40m away from the bank he finds that the angle of elevation to be 30∘.Find 

(i) the height of the tree.

(ii)the width of the river

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Let the height of the tree = h
Let the width of the river =w
Angle of elevation when standing on the bank = 60∘
When moved 40 m away from the bank, angle of elevation = 60∘

Now, tan∠ of elevation=\(height\over distance\)

now tan60 =\(h\over w\)

tan60=\(\sqrt3\)

h=w\(\sqrt3\)           -(1)

Also tan30=\(h\over w+40\)

h=\(w+40\over\sqrt 3\)      -(2)

from equation  1 and 2

\({w\sqrt3}={ w+40\over \sqrt3}\)

\(3w=w+40\)

w=20 m

And , height =\(w\sqrt3=20\sqrt3m=34.6m\)

 

Height of the tree=34.64 m and width of the river=20m

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