Question

A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he covers 40 metres away from the bank, he finds the angle of elevation to be 30°.Find the height of the tree and the width of the river. What skill is used by the
person?;​

Answer 1

Answer:

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Answer 2

Let CD=h be the height of the tree and BC=x be the breadth of the river.

From the figure ∠DAC=30°

and ∠DBC=60°

In right angled triangle △BCD , tan60°

= BC/DC

⇒ √3 = h/x

⇒ h = x√3 ..... ( 1 )

From the right-angled triangle △ACD

tan 30° = h / 40+x

⇒ 1/√3 = h / 40+x

√3h = 40 + x ....... ( 2 )

From (1) and (2) we have

√3(x√3) = 40 + x

⇒ 3x = 40 + x

⇒ 3x − x = 40

⇒2x=40

⇒x = 20

From (1) we get h = x

h = x√3 = 20√3 = 20 × 1.732 = 34.64 m

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