Question

Two planes take off at the same time from an airport. The first plane is flying at 272 miles per hour on a course of 155. 0°. The second plane is flying in the direction 175. 0° at 336 miles per hour. Assuming there are no wind currents blowing, how far apart are they after 2 hours

Answer 1

The planes are 246.06 miles apart after 2 hours.

According to the question, Two planes take off at the same time from an airport. The first plane is flying at 272 miles per hour on a course of 155.0° and the second plane is flying at 336 miles per hour on a course of 175.0°.

• The distance covered by the first plane in 2 hours (a) = 272 * 2

                                          a = 544 miles

• The distance covered by the second plane in 2 hours (b) = 336 * 2

                                           b = 672 miles

• The angle of the first plane from the ground (x) = 180 - 155

                                           x = 25°

• The angle of the second plane from the ground (y) = 180 - 175

                                            y = 5°

• So, The angle between the two planes (C) ⇒ x - y = 25 - 5

                                            C = 20°

Using the law of cosines, we can calculate the distance between the two planes.

               Law of cosines ⇒  $c^{2} = a^{2} + b^{2} - 2ab.cosC$    → 1

Substitute a = 544, b = 672 and C = 20° in 1, then we get

                           $c^{2} = 544^{2} + 672^{2} - 2(544)(672).cos(20)$

                               =  295936 + 451584 - 2(365568).(0.9396)

                               =  747520 - (731136).(0.9396)

                               =  747520 - 686975.3856

                           $c^{2}$  =  60544.6144

                           c = $\sqrt{60544.6144}$

                           c = 246.058 ≅ 246.06

Therefore, the distance between the two planes after two hours is 246.06 miles.

To know more about distance problems refer to:

https://brainly.com/question/28384268

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