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

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.
.
π/6 = 30 deg = turn from north towards the east.
supplementary angle (inside triangle formed) = (180 - 30) = 150 deg
.
This forms a 50 Km, 50 Km, side_c triangle with the angle between the
two 50 Km sides = 150 deg.
.
use the law of cosines: where C = 150 deg
.
c� = a� + b� − 2abcos[C]
c� = (50)� + (50)� − 2(50)(50)cos[150] ... cos[150] = (-√3)/2
c� = 5000 + 2500(√3)

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