A person standing on the bank of a river observe that
the angle sublended
is food when he retroaked som from the bank he
by a tree on the opposite bank
find the angle to be to find the height of the tree
and
Answers
Answer:
Breadth of the river = 10 meter
Height of the tree =\bold{10\sqrt{3}}10
3
Solution:
A person standing on bank sees the branch of the tree of the opposite to be 60 degree
If the person retreats 20m back he then face the branch at 30 degree as we can see in the diagram attached.
Height of branch from ground = h
Let x be the length of river at which tree forms 60 degree.
To find: Height and breadth of the branch and river.
\tan\ 60^{\circ}=\frac{h}{x}tan 60
∘
=
x
h
If the person backs 20 m it becomes \tan\ 30^{\circ}=\frac{h}{x+20}tan 30
∘
=
x+20
h
\begin{gathered}\begin{array}{l}{\tan 60^{\circ}=\sqrt{3}} \\\\ {\tan 30^{\circ}=\frac{1}{\sqrt{3}}}\end{array}\end{gathered}
tan60
∘
=
3
tan30
∘
=
3
1
Substituting the values we get
\begin{gathered}\begin{array}{l}{\sqrt{3}=\frac{h}{x}} \\ \\{\frac{1}{\sqrt{3}}=\frac{h}{x+20}} \\ \\{h=\sqrt{3} x} \\ \\{x+20=\sqrt{3} h}\end{array}\end{gathered}
3
=
x
h
3
1
=
x+20
h
h=
3
x
x+20=
3
h
Substituting the value of h in x+20=\sqrt{3} hx+20=
3
h
x+20=\sqrt{3} \sqrt{3} xx+20=
3
3
x
3x = x + 20
2x = 20
x = 10
\bold{h=10 \sqrt{3}}h=10
3
Step-by-step explanation:
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Step-by-step explanation:
Let AB be the breadth of the river and BC be the height of the tree which makes a ∠ of 60°
at a point A on the opposite bank.
Let D be the position of the person after retreating 20 m from the bank.
Let AB =x metres and BC =h metres.
We know, tan(θ) = Opposite / Adjacent
From right ∠ed △ ABC and DBC,
we have tan60
∘
=
AB
BC
and tan30
∘
=
20+x
h
⇒
3
=
x
h
and
3
1
=
x+20
h
⇒h=x
3
and h=
3
x+20
⇒x
3
=
3
x+20
⇒3x=x+20⇒x=10m
Putting x=10 in h=
3
x, we get
h=10
3
=17.32m
Hence, the height of the tree =17.32 m and the breadth of the river =10 m.