Two planes take off at the same time from an airport. The first plane is flying at 246 miles per hour on a course of 130.0°. The second plane is flying in the direction 165.0° at 359 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete.
A)423 miles
B)421 miles
C)427 miles
D)431 miles
E)429 miles

Question

Two planes take off at the same time from an airport. The first plane is flying at 246 miles per hour on a course of 130.0°. The second plane is flying in the direction 165.0° at 359 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours? Apply the rules regarding the use of significant digits after all computations are complete.
A)423 miles
B)421 miles
C)427 miles
D)431 miles
E)429 miles

Quizplus · Accepted Answer

The correct answer is A.The first plane travels 246 miles per hour on a course of 130.0°. After 2 hours, it has traveled 246 miles * 2 hours = 492 miles.The second plane travels 359 miles per hour on a course of 165.0°. After 2 hours, it has traveled 359 miles * 2 hours = 718 miles.The distance between the two planes is the hypotenuse of a right triangle with legs of 492 miles and 718 miles. Using the Pythagorean theorem, we can find the distance between the two planes:```distance = sqrt(492^2 + 718^2) = 866 miles```Rounding to the nearest mile, the distance between the two planes after 2 hours is 866 miles.

Two Planes Take Off at the Same Time from an Airport