Answer:
245.1° and 13 knots
Explanation:
The given parameters are;
The true heading = 135°
The resultant ground track = 130°
The true airspeed = 135 knots
The ground speed = 140 knots
Given that the true airspeed the ground speed and the wind direction and magnitude form a triangle, we have;
From cosine rule, we have;
a² = b² + c² - 2×b×c×cos(A)
Where
a = The magnitude of the wind speed in knot
b = The true airspeed = 135 knots
c = The ground speed = 140 knots
A = The angle in between the true heading and the resultant ground track heading = 5°
Which gives;
a² = 135² + 140² - 2×135×140×cos(5 degrees) = 168.84 knots²
a = √168.84 = 12.9934 ≈ 13 knots
We have;
135 × sin(135 degrees) - 140× sin(130 degrees) = -11.7868
135 × cos(135 degrees) - 140× cos(130 degrees) = -5.469
Tan(θ) = -11.8/-5.5 = 2.155
θ = tan⁻¹(2.155) = 65.108°
Given that the wind is moving in opposite direction (slowing down the airplane, we add 180°, to get
Therefore, the angle direction = 180 + 65.108 = 245.1
Therefore, we have;
245.1° and 13 knots
