Question

two ships are approaching a lighthouse from opposite directions the angle of depression of two ships from the lighthouse are 30 degree and 40 Degree . if the distance between two ships is 100 . find the height of the lighthouse.​

Answer 1

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