Question

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 20metres back, he sees the top at on elevation of 30°.

draw a rough figure and find the height of the tree?

what is the width of the river?
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Answer 1

Answer:

Step-by-step explanation:

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 =x  

h ​⇒h=x  3

 .....(1)

From the right-angled triangle △ACD

tan30∘ = 40+x

h ⇒  3 1  =  40+x

h ⇒  3 h=40+x           .......(2)

From (1) and (2) we have

3 (x 3  )=40+x

⇒3x=40+x

⇒3x−x=40

⇒2x=40

⇒x=  2

40  =20

From (1) we get h=x  

3 =20  

3  =20×1.732=34.64m

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