Two ships are sailling in the sea on the two sides of a lighthouse. If the distance between the ships is 10 3 + 1 meters and their angle of elevations of the top of the lighthouse are 60 o and 45 o , then the height of the lighthouse is (The two ships and the foot of lighthouse are in a straight line)

Question

Two ships are sailling in the sea on the two sides of a lighthouse. If the distance between the ships is 10 3 + 1 meters and their angle of elevations of the top of the lighthouse are 60 o and 45 o , then the height of the lighthouse is (The two ships and the foot of lighthouse are in a straight line), 20 meters, 20 3 meters, 10 3 meters, 5 3 meters

MARKS App · Accepted Answer

Let, A C is the lighthouse and the ships are at B and D . In Δ A B C, A C B C = tan ⁡ 60 o {where, A C = h meters = height of lighthouse} h B C = 3 ⇒ B C = h 3 meters In Δ A C D, A C C D = tan ⁡ 45 o ⇒ h C D = 1 ⇒ C D = h B C + C D = h 3 + h = 10 3 + 1 ⇒ h = 10 3 meters

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