An airplane is flying in a direction of 75 degrees north of east at a constant flight speed of 300 miles per hour. Th wind is blowing due west at a speed of 25 miles per hour. What is the actual direction of the airplane? Round your answer to the nearest tenth. Show your work

The resultant speed is 294.5 mi/h in a direction N79.7°E

Step-by-step explanation:

Let

East and North as the positive x and y-axis, respectively.

West and South as the negative x- and y-axis, respectively. 

step 1

Take the x- and y-components of the speeds. 

Airplane:

Wind:

step 2

Adding up the components:

step 3

Find the resultant speed

step 4

Find the direction

substitute

therefore

The resultant speed is 294.5 mi/h in a direction N79.7°E