SOLUTION: A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50 km. Without using a calculator, determine an e
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Question 617271: A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50 km. Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A cruise ship sailed north for 50 km. Then, the captain turned the ship eastward through an angle of pi/6 and sailed an additional 50 km. Without using a calculator, determine an exact expression for the direct distance from the start to the finish of the cruise.
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π/6 = 30 deg = turn from north towards the east.
supplementary angle (inside triangle formed) = (180 - 30) = 150 deg
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This forms a 50 Km, 50 Km, side_c triangle with the angle between the
two 50 Km sides = 150 deg.
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use the law of cosines: where C = 150 deg
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c² = a² + b² − 2abcos[C]
c² = (50)² + (50)² − 2(50)(50)cos[150] ... cos[150] = (-√3)/2
c² = 5000 + 2500(√3)
