On both sides of a lighthouse, two ships are cruising in the water. From the ships, the angle of elevation of the top of the lighthouse is 30° and 45°, respectively. The distance between the two ships is: If the lighthouse is 100 metres high, the distance between the two ships is:
A. 173 m
B. 200 m
C. 273 m
D. 300 m
Answer:C
On both sides of a lighthouse, two ships are cruising in the water. From the ships, the angle of elevation of the top of the lighthouse is 30° and 45°, respectively. The distance between the two ships is: If the lighthouse is 100 metres high, the distance between the two ships is:
A. 173 m B. 200 m C. 273 m D. 300 m
Explanation: Assume AB is the lighthouse and C and D are the ship positions.Then ADB = 45°, ACB = 30°, and AB = 100 m.AB/AC = tan 30° = 1/ ROOT 3, AC = AB x 3 = 100/ ROOT3 m AB/AC = tan 30° = 1/ ROOT 3 m,AB/AD = tan 45° = 1 AD = AB = 100 m AB/AD = tan 45° = 1 AD = AB = 100 m,(100/ ROOT3 + 100) m = 100 ROOT 3 + 1) = (100 x 2.73) m = 273 m CD = (AC + AD) = (100/ ROOT3 + 100) m = 100 ROOT 3 + 1) = (100 x 2.73) m = 273 m