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15 Dec 2020, 09:45
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C
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Difficulty:
65%
(hard)
Question Stats:
54% (02:21) correct
46%
(02:56)
wrong
based on 37
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Two planes depart at the same time from the same terminal, one traveling due north and the other due west, each on a straight flight path. When the shortest distance between the planes is 40 miles, one plane would need to turn 120° to either the left or right to point directly at the other plane. Which of the following most closely approximates the number of miles the faster of the two planes has traveled at this point in time?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
15 Dec 2020, 20:31
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Bunuel
Two planes depart at the same time from the same terminal, one traveling due north and the other due west, each on a straight flight path. When the shortest distance between the planes is 40 miles, one plane would need to turn 120° to either the left or right to point directly at the other plane. Which of the following most closely approximates the number of miles the faster of the two planes has traveled at this point in time?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Please refer to the diagram below. The shortest distance is the Hypotenuse of the triangle. Assuming the the plane going west rotates 120 degrees. The triangle ABC so formed, then becomes a 30 - 60 - 90 triangle.
The side opposite 60 degrees = \(\frac{\sqrt{3}}{2} * hypotenuse = \frac{\sqrt{3}}{2} * 40 = 20\sqrt{3} = 34.64 \space or \approx 35\) miles
The side opposite 30 degrees = \(\frac{1}{2} * hypotenuse = \frac{1}{2} * 40 = 20\) miles
Option C
Arun Kumar
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19 Dec 2020, 21:28
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Since, one angle of turn = 120 degree,
So, in triangle, it makes 60 degree, hypotenuse is 40 miles.
Hence side= Sqrt(3)/2 * 40 ~35 miles.
Ans. C.
So, in triangle, it makes 60 degree, hypotenuse is 40 miles.
Hence side= Sqrt(3)/2 * 40 ~35 miles.
Ans. C.
