Question

From the top of a lighthouse, the angles of depression of two ships are 60" and 30". The ships are along the same straight line with the lighthouse and are on the same side of it. If the ship nearer to the lighthouse is 150 m away from it find the distance between the lighthouse and the other ship and the height of the lighthouse.​

Answer 1

Answer:

Solution

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Let AB be the lighthouse and the two ships be at point C and D respectively.

⇒ In △ABC,tan45

o

=

BC

AB

⇒ 1=

BC

150

∴ BC=150m

⇒ In △ABD,tan30

o

=

BD

AB

⇒

3

1

=

150+CD

150

⇒ 150

3

=150+CD

⇒ CD=150(

3

−1) m=109.5 m (Take

3

=1.73)

∴ The distance between two ships is 109.5m

solution