Question

An airplane flying at 600 miles per hour has a bearing of 53°. After flying for 2.5 hours, how far north and how far east will the plane have traveled from its point of departure? (Round your answers to the nearest whole number.)

Answer 1

Answer:

Eastward distance of airplane = 903 miles

Northward distance of airplane = 1198 miles

Step-by-step explanation:

Consider the sketch attached below.

Let the Eastward distance be represented by x

let the Northward distance be represerted by y

The distance traveled = speed of plane x time

= 600 x 2.5 = 1500 miles  

from basic trigonometry of a right angled triangle we have that

$sin(53)=\frac{x}{1500}$

$x=1500\timessin(53) \approx 903 miles$

$cos (53) = \frac{y}{1500}$

$y= 1500cos(53)\approx1198 miles$

∴ Northward distance = 1198 miles

   Eastward distance =903 miles