40. The angles of depression of the top and bottom of a 8 m tall building
from the top of a tower are 30° and 45° respectively. Find the height of
the tower and the distance between the tower and the building.
(CBSE 2019C)
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Answers
Step-by-step explanation:
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ANSWER
Let AB and CD be the multi-storied building and the building respectively.
Let the height of the multi-storied building be hm and the distance between the two building be xm
AE=CD=8m [ Given ]
BE=AB−AE=(h−8)m and
AC=DE=xm [ Given ]
Now, in △ACB,
⇒ tan45
o
=
AC
AB
⇒ 1=
x
h
∴ x=h ---- ( 1 )
In △BDE,
⇒ tan30
o
=
ED
BE
⇒
3
1
=
x
h−8
∴ x=
3
(h−8) ------ ( 2 )
⇒ h=
3
h−8
3
⇒
3
h−h=8
3
⇒ h(
3
−1)=8
3
⇒ h=
3
−1
8
3
⇒ h=
3
+1
8
3
×
3
+1
3
+1
⇒ h=
3−1
8
3
(
3
+1)
⇒ h=
2
8
3
(
3
+1)
∴ h=(12+4
3
)m
∴ x=(12+4
3
)m [ From ( 1 ) ]
∴ The height of the multi-storied building and the distance between the two buildings is (12+4
3
)m
solution
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