10. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff. At a point on the plane, 30 metres away from the tower, an observer notices that the angles of elevation of the top and bottom of the flagstaff are 60 and 45° respectively. Find the height of the flagstaff and that of the tower.
Answers
Answered by
1
In △CBD,tan30
o
=
BC
BD
⇒
3
1
=
x
h
⇒ x=
3
h ----- ( 1 )
⇒ In△ABC,tan45
o
=
BC
AB
⇒ 1=
x
7+h
⇒ x=7+h
⇒
3
h=7+h [ From ( 1 ) ]
⇒
3
h−h=7
⇒ (
3
−1)h=7
⇒ h=
3
−1
7
⇒ h=
3
−1
7
×
3
+1
3
+1
∴ h=
3−1
7(
3
+1)
=
2
7(1.73+1)
=9.55m
∴ Height of the tower is 9.55m.
solution
Answered by
41
Let,
- BC be the tower
- AB be the flagstaff
Given:-
- CD = 30m
- AB = h
- BC = x
In ∆ADC,
Tan60° = √3 = (h+x)/30
⇢ h + x = 30√3
⇢ x = 30√3 - h .....i)
In ∆BCD,
Tan45° = 1 = x/30
➝ (30√3 - h)/30 = 1 (from i)
➝ 30√3 - h = 30
➝ h = 30√3 - 30....ii)
➝ h = 51.96 - 30
➝ h = 21.96m
⇝ x = 30√3 - h
⇝ x = 30√3 - (30√3 - 30)
⇝ x = 30√3 - 30√3 + 30
⇝ x = 30m
Hence,
• Height of flagstaff = 21.96 m
• Height of tower = 30 m
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