a) 105
D)
c) 5m
c) 135 feets
d) 150 feets
One or more than one correct answer type questions :
3
3
th portion of a vertical pole subtends an angle o such that tan 8 =
34. The upper
4.
at a point in the
5
horizontal plane through its foot and at a distance 40m from the foot. Find the possible height of the
vertical pole
[ ]
80
b) 160m
d) 100 m
a) 40m
91
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ANSWER
Given that,
α=tan
−1
5
3
tanα=
5
3
And we know that In the above figure,
tanβ=
OA
AC
=
4×40
h
=
160
h
Now, In ΔAOB,
tan(α+β)=
OA
AB
=
40
h
⇒tan(α+β)=
1−tanαtanβ
tanα+tanβ
⇒
40
h
=
1−
160
h
×
5
3
160
h
+
5
3
⇒
40
h
=
800
800−3h
160
h+96
⇒
40
h
=
160
h+96
×
800−3h
800
⇒
40
h
=
800−3h
5(h+96)
⇒800h−3h
2
=200(h+96)
⇒800h−3h
2
=200h+19200
⇒3h
2
−600h+19200=0
⇒h
2
−200h+6400=0
⇒(h−160)(h−40)=0
⇒h−160=0,h−40=0
⇒h=160andh=40
Hence h=40m. be the height of pole and less then 100m.
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