Question:
Two boats leave the same bank of sea at the same time. One goes 12km per hour in the direction N550E and other goes 16km per hour in the direction S650E. Find the distance between the boats at the end of two hours.
Answer:
Distance travelled by boats after 2 hours
Boat A = 2*12 = 24 km
Boat B = 2*16 = 32 km
Now, ∠ACB = 180 - (55 + 65) = 180 - 120 = 60
Applying cosine formula,
c2 = a2 + b2 - 2ab* cos C
=> c2 = 322 + 242 - 2*32*24*cos 60
=> c2 = 1024 + 576 - 2*32*24*(1/2)
=> c2 = 1024 + 576 - 32*24
=> c2 = 1600 - 768
=> c2 = 832
=> c = √832
=> c = 28.84
Hense, the distance between the two boats is 28.84 km
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