Arturo O. answered • 08/13/16
Tutor
5.0
(66)
Experienced Physics Teacher for Physics Tutoring
The law of cosines may be used to solve this. I will try to explain without a diagram.
Side a: a = 610*1.5 miles = 915 miles
Side b: b = 610*2 miles = 1220 miles
Side c: This is what we want to solve for.
θ = angle opposite to side c, i.e. the angle between sides a and b.
θ = (180 - 10) degrees = 170 degrees
Law of cosines:
c2 = a2 + b2 - 2ab*cosθ
c2 = (915)2 + (1220)2 - 2(915)(1220)*cos170 ≅ 4524000 miles2
c ≅ 2127 miles
Tom K.
nice work, Arturo.
It's always a good idea to make sure an answer is reasonable. Note that, as the plane flies a total of 1 1/2 + 2 = 3 1/2 hours, we know the distance should be less than 610 * 3.5, but not much, since it was only a small turn. 610*3.5 =
2135 is indeed slightly bigger than the answer.
Report
08/14/16
Arturo O.
Yes Tom, that is the triangle inequality: The length of any side is always smaller than the sum of the lengths of the other two sides. But in this case, since the turn is only 10º, the long side is
almost as large as the sum of the other two sides.
Report
08/14/16
Russell W.
08/13/16