An observer on the top of a cliff 20 m above the sea level observes the angles of depression of two ships to be 45° and 30° respectively. Find the distance betwee ships, of the ships are:
(i) on the same side of cliff
(ii) on the opposite sides of cliff.
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for part i)and ii) refer the photos above
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The distance between ships 14.64 m if on the same side of cliff & 54.64 m if on the opposite sides of cliff.
Step-by-step explanation:
Tan α = Height of cliff/ Horizontal Distance from cliff
Tan 45 = 20/Distance of Ship from Cliff
=> 1 = 20/Distance of Ship from Cliff
=> Distance of Ship from Cliff = 20
Tan 30 = 20/Distance of Ship from Cliff
=> 1/√3 = 20/Distance of Ship from Cliff
=> Distance of Ship from Cliff = 20√3
(i) on the same side of cliff
Distance between Ships = 20√3 - 20 = 20 (√3 - 1) m = 14.64 m
(ii) on the opposite sides of cliff
Distance between Ships = 20√3 + 20 = 20 (√3 + 1) m = 54.64 m
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