sir this is the question from the book -ML aggarwal( avichal publication) class 10th , chapter20 , heights and distances
this question once has been asked in exam . and have chances to come in future .
we know A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600;
when he retires 20 m from the bank,
he finds the angle to be 300.
wehave to Find the height of the tree and the breadth of the river.
question no 17 , heights and distances , ICSE board
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A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 600; when he retires 20 m from the bank, he finds the angle to be 300. Find the height of the tree and the breadth of the river.
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Consider TR as the tree and PR as the width of the river.
Take TR = X and PR = y
In right triangle TPR
tan θ = TR/PR
Substituting the values
tan 600 = x/y
So we get
√3 = x/y
x = y √3…… (1)
In right triangle TQR
tan 300 = TR/QR
tan 300 = x/(y + 20)
We get
1/√3 = x/(y + 20)
x = (y + 20)/ √3 ….. (2)
Using both the equations
y√3 = (y + 20)/ √3
So we get
3y = y + 20
3y – y = 20
2y = 20
y = 10
Now substituting the value of y in equation (1)
x = 10 × √3 = 10 (1.732) = 17.32
Hence, the height of the tree is 17.32 m and the width of the river is 10 m.