A person standing on the bank of a river observe that the angle of elevation of the top of a tree standing on opposite bank is 60 degree when he moves 30m away from the bank he finds the angle of elevation to be 30 degree find the height of the tree and width of the river taken under root 3 is equal to 1.732
Answers
height of the tree is 25.98 m and the width of the river is 15m
answr
search
What would you like to ask?
10th
Maths
Some Applications of Trigonometry
Heights and Distances
A person standing on the ba...
MATHS
avatar
Asked on December 27, 2019 by
Saakshi Bisariya
A person standing on the bank of the river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60
∘
.When he was 40m away from the bank he finds that the angle of elevation to be 30
∘
.Find
(i) the height of the tree.
(ii)the width of the river,correct to 2d.p
HARD
Help best friend
Study later
ANSWER
Let CD=h be the height of the tree and BC=x be the breadth of the river.
From the figure ∠DAC=30
∘
and ∠DBC=60
∘
In right angled triangle △BCD,tan60
∘
=
BC
DC
⇒
3
=
x
h
⇒h=x
3
.....(1)
From the right-angled triangle △ACD
tan30
∘
=
40+x
h
⇒
3
1
=
40+x
h
⇒
3
h=40+x .......(2)
From (1) and (2) we have
3
(x
3
)=40+x
⇒3x=40+x
⇒3x−x=40
⇒2x=40
⇒x=
2
40
=20
From (1) we get h=x
3
=20
3
=20×1.732=34.64m
∴ Height of the tree=34.64 m and width of the river=20m