A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50 m away from the bank, he finds the angle of elevation to be 30°. Calculate: (1) the width of the river and the height of the tree.
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10th
Maths
Some Applications of Trigonometry
Heights and Distances
A person standing on the ba...
MATHS
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
o
. When he moves 40 m away from the bank. he finds the angle of elevation to be 30
o
. Find the height of the tree and width of the river. (
3
=1.73)
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ANSWER
Let AB be a tree height x m.
i.e. AB=x and BC=y (let)
In right angled triangle ABC,
∠ACB=60
o
⇒tan60
o
=
BC
AB
3
=
y
x
∴x=
3
y ...(i)
In right angled triangle ABD,
∠ADB=30
o
⇒tan30
o
=
BD
AB
3
1
=
y+40
x
∴x=
3
y+40
....(ii)
From equations (i) and (ii)
3
y=
3
y+40
3y=y+40
⇒2y=40
⇒y=20
From equation (i),
x=
3
y=20
3
=20×1.73=34.6
Hence, the height of the tree is 34.6 m and the width of the river is 20 m.