Question

A plane is flying 225 mph heading South 25°West. The wind is blowing South 80°East at 60 mph.

What is the bearing of the plane?
What is the smallest angle of the triangle?
What is the largest angle of the triangle?
What is the remaining angle of the triangle?
What is the ground speed of the plane?

Answer 1

Vp=225mi/h@(270-25) + 60mi/h@(270+80).
Vp = 225mi/h@245deg + 60mi/h@350deg.
Vp=(225cos245+60cos350) +
i(225sin245+60sin350).

Vp = (-95.1+59.1) + i(-203.9-10.4),
Vp = -36 - i214.3,

1. tan(Ar) = -214.3 / -36 = 5.95,
Ar = 80.5deg.
A = Ar + 180 = 80.5 + 180 = 260.5deg. =
Direction(bearing).

2. 90 - Ar = 90 - 80.5 = 9.5deg. = smallest angle.

3. 90deg = Largest angle.

4. 90 - 9.5 = 80.5deg.

5. Vp^2 = (-36)^2 + (214.3)^2 = 47,220.49,
Vp = 217.3mi/h.