The plane is off course at 2.41 degrees and the groundspeed of the aircraft is 572.4 km/hr.
According to the law of sine, or sine law, the ratio of a triangle's side length to the sine of the opposing angle remains constant for all three sides. The sine rule is another name for it.
The Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the lengths of the other sides minus twice the product of the other two sides multiplied by the cosine of the angle that separates them.
The problem can be drawn as:
The red arrow here shows the resultant vector.
We will use the cosine rule because we have side angle side triangle
[tex]a^{2} =b^{2}+c^{2} -2bccos A[/tex]
This becomes:
[tex]R^{2}=600^{2}+40^{2}-2(600)(40)(cos 45)\\R^{2}=360000+1600-48000(0.707)\\R^{2}=361600-33936\\R=572.4 km/hr[/tex]
This is the groundspeed of the aircraft.
To find θ, use sine rule:
[tex]\frac{sin C}{c} =\frac{sin A}{a}[/tex]
This becomes:
sinθ/40= sin(45)/572.4
sinθ= [tex]\frac{0.707}{572.4}[/tex]
sin θ= 0.04207
θ = 2.41 degree
Therefore, the plane is off course at degrees 2.41.
To know more about sine and cosine rule, visit: https://brainly.com/question/17289163
#SPJ4
