Q20 of 46 Page 1

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

We have


Here, let height of the lighthouse be h meters.


Let distance between first ship and foot of the lighthouse be BC = x meters.


Given: Distance between the two ships is CD = 200 meters.


∠ACB = 45°, ∠ADB = 30°


To find: height of the lighthouse, i.e., h.


We know


In ∆ACB,



⇒ 1 = h/x [∵, tan 45° = 1]


⇒ x = h …(i)


In ∆ADB,



⇒ [by equation (i) and also since, tan 30° = 1/√3]


⇒ 200 + h = √3h


⇒ √3h – h = 200


⇒ (√3 – 1)h = 200


⇒


By rationalizing it, we get



⇒


⇒ h = 100(1.73 + 1) = 100 × 2.73 = 273


Hence, height of the lighthouse is 273 m.


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