A scholar reaching a river bank enquired about the depth of the river. He was told that near one bank it was 60 centimeters deep, in the middlle 270 centimeters and near the other bank, 60 centimeters. He calculated the average: 60+270+60/3 =130 cm The scholar, who was 180 centimeters tall, was relieved. The average depth was less than his height. The scholar, who couldn't swim, started crossing the river. What would have happened?
Answers
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Class 10
>>Maths
>>Some Applications of Trigonometry
>>Heights and Distances
>>A person standing on the bank of a river
Question
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A person standing on the bank of a river observes that the angle of elevation with a tree on the opposite bank is 60
0
. When he retired 40 metres from the bank perpendicular to it, he finds the angle to be 30
0
. The breadth of river and the height of the tree (in metres) are
Medium
Solution
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Correct option is C)
d=40 m
tan60
0
=
b
h
=
3
...(i)
tan30
0
=
d+b
h
⇒
3
1
=
d+b
h
⇒
3
=
h
d+b
... (ii)
From (i) and (ii), we get
3=
b
d+b
⇒3=
b
d
+1
⇒2=
b
d
⇒b=
2
d
=20 m
h=
3
b=20
3
m
Answer:
His 130cm will be under the water and 50 cm will be out of water