The actual direction of the plane is 75° North of west with a speed of 275 mph
<u>Explanation:</u>
Speed of airplane = 300mph
Direction of airplane = (300 cos 75° , 300 sin 75°)
Speed of wind = 25 mph
If the wind is blowing due east then the angle is = 90° + (90 - 75)
= 105°
Direction of wind = (25 cos 105° , 25 sin 105°)
So,
Direction of plane + Direction of wind = Actual Direction of airplane
(300 cos 75° , 300 sin 75°) + (25 cos 105° , 25 sin 105°) = (x, y)
( 77.65 , 289.78 ) + ( -6.47 , 24.15 ) = (x, y)
(71.18, 265.63 ) = (x, y)
Speed =
Direction:
Therefore, the actual direction of the plane is 75° North of west with a speed of 275 mph