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Question

The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be 45 and 30 respectively. If the ships are 200 m apart, find the height of the lighthouse.

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Solution



Let CD be the lighthouse and A and B be the positions of the two ships.
AB=200 m (Given)

Suppose CD=h m and BC=x m
Now, DAC=ADE=30 (Alternate interior angles)

DBC=EDB=45 (Alternate interior angles)

In right BCD, we have

tan45=CDBC

1=hx

h=x

In right ACD, we have

tan30=DCAC

13=hx+200

h3=x+200

h3=h+200

h=20031

h=100(3+1) m


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