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57.73 m/min
Step-by-step explanation:
Let the speed of the boat be 'x' metre per minute.
Let AB be the lighthouse and C,D be the positions of boat such that AB = 100 m,CD = 2x.
∠ADB = 30° and ∠ACB = 60°.
(i) In ΔADB:
AB/DB = tan 30°
⇒ 100/DB = (1/√3)
⇒ BD = 100√3
(ii) In ΔABC:
(AB/BC) = tan 60°
⇒ 100/BC = √3
⇒ BC = (100/√3)
∴ CD = BD - BC
⇒ 2x = (100√3) - (100/√3)
⇒ 2x = (300 - 100)/√3
⇒ 2x = 200/√3
⇒ x = 100/√3
⇒ x = 100/1.732
⇒ x = 57.73 m/min.
Therefore, Speed of the boat is 57.73 metre per minute.
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