Two ships are approaching a lighthouse from opposite directions

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Two ships are approaching a light-house from opposite directions. The angles of depression of the two ships from the top of the light-house are 30o and 45o. If the distance between the two ships is 100 m, find the height of the light-house. [Use 3 = 1.732]

Answered by admin @


Please refer to the given diagram.
AB = 100
Let AC = x
Let BC = 100-x
Let CD = h
In ΔEAD,
EA = DC
ED = AC
tan 45° = EA/ED
1 = h/x
x = h
In ΔDFB
FB = CD
DF = CB
tan 30° = FB/DF
1/√3 = h/100-x
1/√3 = h/100-h
100-h = √3h
100-h = 1.732h
2.732h = 100
h = 100/2.732
h = 36.603m
h = 36.6m

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