Question

a person standing on the bank of a river observes that the angle of elevation of the top of a tower standing on the opposite bank is 60°. When he moves 40m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tower and width of the river.

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Answer 1

Answer:

ln right triangle BCD,we have

tan 60°=CD/BC

=> √3=h/x

=> x=h/√3 ......(1)

ln right triangle ACD,we have

tan 30°=CD/AC

=> 1/√3=h/x+40

=> x+40=√3 h

=> x=√3h-40 ......(2)

comparing (1) and (2) ,we get

h/√3=√3h-40

=>h=3h-40√3

=> -2h=-40√3

=>h=20√3

=20×1.732

=34.64metres

Hence, the height of the tree is 34.64metres.

now substituting the value of

h=20√3

in (1) we get

x= h/√3

=>x=20√3/√3

=>x=20m

Hence, the width of the river is 20m.

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