# A person standing on the bank of the river observes that the angle of elevation of the top of a tree

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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