the circumference of a circular pond is 176 and A pillar is fixed at the centre of the pond if a person finds the angle of elevation of 60 degree of the top of the pillar from any point on the bone find the height of the pillar above the water level
Answers
Answer:
ANSWER
Let the height of pillar CD=h f t
Given that distance AB=100 ft
Let B to C distance BC=xft
then
Total AC=AB+BC=(100+x)ft
In △BCD,
BC
CD
=tanθ
x
h
=tan30
∘
x
h
=
3
1
x=h
3
.....(1)
Now, In △ACD,
AC
CD
=tanθ
100+x
h
=tan15
∘
100+x
h
=tan(45−30)
100+x
h
=
1+tan45
∘
tan30
∘
tan45
∘
−tan30
∘
∴tan(A−B)=
1+tanA
tanA−tanB
100+x
h
=
1+1×
3
1
1−
3
1
100+x
h
=
(
3
)
2
−1
2
(
3
−1)
2
100+x
h
=
3−1
(
3
)
2
+1
2
−2
3
100+x
h
=
2
4−2
3
100+x
h
=2−
3
Put the value of x=h
3
Then,
100+h
3
h
×
1
2−
3
h=(2−
3
)(100+h
3
)
h=200+2
3
h−100
3
−3h
h+3h−2
3
h=200−100
3
4h−2
3
h=100(2−
3
)
2h(2−
3
)=100(2−
3
)
2h=100
h=
2
100
h=50 ft
Hence, the height of pillar is CD=h=50 ft.
Answer:
height is 50
Step-by-step explanation:
hence the height pillars is is CD=h=50feets
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