SOLUTION: An airplane flies 200 miles from point A in the direction 115� and then travels in the direction 210� for 80 miles. Approximately how far is the airplane from A? (Round your answer

Question 812597: An airplane flies 200 miles from point A in the direction 115� and then travels in the direction 210� for 80 miles. Approximately how far is the airplane from A? (Round your answer to the nearest whole number.)
Found 2 solutions by TimothyLamb, stanbon:
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
use the law of cosines to find the third side of the triangle
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a^2 = b^2 + c^2 - 2bc cos(t)
where:
b = 220
c = 80
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but first find the included angle t
t = 210 - 115 = 95 degrees
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a^2 = 220^2 + 80^2 - 2*220*80 cos(95)
a^2 = 48400 + 6400 - 2*220*80*(-0.0871557)
a^2 = 48400 + 6400 - 2*220*80*(-0.0871557)
a^2 = 51732.118
a = 227.45
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Answer:
the airplane is about 227.5 miles from its departure point
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Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
An airplane flies 200 miles from point A in the direction 115� and then travels in the direction 210� for 80 miles.
Approximately how far is the airplane from A?
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Assume A is the point (0,0)
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Assume the end point of travel is (x,y)
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x-coordinate:: 200*cos(115)+80*cos(210) = -153.8
y-coordinate:: 200*sin(115)+80*sin(210) = 141.26
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distance from A to (x,y) = sqrt[153.8^2+141.26^2] = 208.82 miles
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Cheers,
Stan H.
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