A ship of height 24 m is sighted from a light house. From the top of the light house the angle
of depression of the top of the mast and base of the ship is 30o
and 45o
respectively. How
far is the ship from the light house ? ( 3 = 1.73
Answers
Let AB be the lighthouse and CD be the ship. Let the height of the lighthouse be 'h' and let the distance from the ship of the lighthouse is 'x' m. The height of the ship is 24m. The angle of depression to the top of the mast is 30
o
and the angle of depression to the base of the ship is 45
o
.
CE⊥AB.
In ΔABD,
tan45
o
=
x
h
1=
x
h
∴h=x ....(i)
In ΔAEC,
tan30
o
=
EC
AE
=
x
h−24
3
1
=
x
h−24
h−24=
3
x
...(ii)
From equations (i) and (ii), we get
x−24=
3
x
x−
3
x
=24
(
3
−1)x=24
3
x=
3
−1
24
3
=
(
3
−1)(
3
+1)
24
3
(
3
+1)
=
3−1
24(3+
3
)
=12(3+
3
)
=12(3+1.73)
=12×4.73
=56.76
∴ The ship is at a distance of 56.76m from the lighthouse.
solution.
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