the girlstanding on the lighthouse she observed two ship due to east of light house.the angle of depression is 30degree and 60 degree.the distance between two ship 300m. find the height of the light hOuse
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MATHS
A girl standing on a lighthouse built on a cliff near the seashore, observes two boats due East of the lighthouse. The angles of depression of the two boats are 30
∘
and 60
∘
. The distance between the boats is 300m. Find the distance of the top of the lighthouse from the sea level. ( Boats and foot of the lighthouse are in a straight line )
December 26, 2019avatar
Krish Johnson
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ANSWER
Let A and D denote the foot of the cliff and the top of the lighthouse respectively.
Let B and C denote the two boats.
Let h metres be the distance of the top of the lighthouse from the sea level.
Let AB=x metres.
Given that ∠ABD=60
∘
,∠ACD=30
∘
In the right angled △ABD,
tan60
∘
=
AB
AD
⇒AB=
tan60
∘
AD
Thus, x=
3
h
(1)
Also, in the right angled △ACD, we have
tan30
∘
=
AC
AD
⇒AC=
tan30
∘
AD
⇒x+300=
(
3
1
)
h
Thus, x+300=h
3
(2)
Using (1) in (2), we get
3
h
+300=h
3
⇒h
3
−
3
h
=300
∴2h=300
3
. Thus, h=150
3
.
Hence, the height of the lighthouse from the sea level is 150
3
m.
solution