2. A vertical tower stands on a horizontal plane and is surmounted by a
vertical flag staff of height 5m. At a point on the plane, the angles of
elevation of the bottom and the top of the flag staff are 450
and 600
,
respectively. Find the height of the flag staff.
Answers
Answer:
9.55 m
Step-by-step explanation:
⇒ 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.....
MATHS
MATHSA vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7 m. From a point on the plane, the angle of elevation of the bottom of the flag-staff is 30∘ and that of the top of the flag-staff is 45∘. Find the height of the tower.
ANSWER
ANSWER⇒ In △CBD,tan30o=BD/BC
⇒ 31/√3=h/x
⇒ x=√3h ----- ( 1 )
3h ----- ( 1 )⇒ In△ABC,tan45o=AB/BC
⇒ 1=x7+h
⇒ 1=x7+h⇒ x=7+h
⇒ 1=x7+h⇒ x=7+h⇒ √3h=7+h [ From ( 1 ) ]
3h=7+h [ From ( 1 ) ]⇒ √3h−h=7
3h−h=7⇒ (√3-1)h=7
⇒ h=√3−17
3−17⇒ h=√3−17×√3+1√3+1
3+1∴ h=3−17(√3+1)=27(1.73+1)=9.55m
