Answer:
Explanation:
In navigation the angle of the course (on a compass) is counted clockwise from the North (so, the direction to the North is 0°, to the East is 90°, to the South is 180°, and to the West is 270°).
The North on most maps is a vertically up direction.
In coordinate Geometry and Trigonometry, which we will use, angles are measured counterclockwise from the positive direction of the horizontal X-axis (the East on most maps)
Let's make a simple transformation into Trigonometric standard using the direction to the East as an X-axis.:
320° on compass is 90° + ( 360° - 320°) = 130° counterclockwise from the X-axis.
300° on compass is 90° + ( 360° - 300°) = 150° counterclockwise from the X-axis.
This is a problem on addition of two vectors. Each is defined by its amplitude and angle of direction:
airplane (vector A ) has amplitude 335 mph and angle 130°
wind (vector W ) has amplitude 50 mph and angle 150°
To add these two vectors, we represent both as sums of X-component and Y-component:
Ax = 345.cos (130°)
Ay = 345.sin (130°)
Wx = 40.cos(150°)
Wy = 40.sin(150°)
Both X-components act along the same direction, both Y-components act along the same direction. So, we can add X-components to get an X-component of the resulting movement and add Y-components to get a Y-component of the resulting movement.
(A+W)x = Ax + Wx = 345.cos(130°) + 40.cos(130°)
(A+W)y = Ay + Wy = 345.sin(150°) + 40.sin(150°)
Knowing two components of the resulting vector of movement, we can easily determine the amplitude |A+W| and direction ∠(A+W)
|A+W| =√(A+W)²x + √(A+W)²y
∠(A+W) = arctan|(A+W)y
----------
(A+W)x
