A plane flies 650 mph on a bearing of 175.3°. A 25-mph wind, from a direction of 266.6°, blows against the plane. Find the resulting bearing of the plane.

Verified step by step guidance

1. Convert the plane's bearing and the wind's direction from degrees to radians for calculation purposes. Use the formula \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).
2. Determine the components of the plane's velocity vector and the wind's velocity vector. Use the formulas \( V_x = V \cos(\theta) \) and \( V_y = V \sin(\theta) \), where \( V \) is the speed and \( \theta \) is the angle in radians.
3. Calculate the resultant velocity vector by adding the components of the plane's velocity vector and the wind's velocity vector. Use \( V_{rx} = V_{px} + V_{wx} \) and \( V_{ry} = V_{py} + V_{wy} \).
4. Compute the magnitude of the resultant velocity vector using the Pythagorean theorem: \( V_r = \sqrt{V_{rx}^2 + V_{ry}^2} \).
5. Find the resultant bearing of the plane by calculating the angle of the resultant velocity vector. Use the formula \( \theta_r = \tan^{-1}(\frac{V_{ry}}{V_{rx}}) \) and convert the angle from radians back to degrees.