Answer:
The resultant velocity is 86.1 mi/h.
Explanation:
The law of cosines is given by:
[tex] c^{2} = a^{2} + b^{2} - 2abcos(\theta) [/tex]
Where:
c: is the resultant velocity =?
a: is the velocity of the plane = 75.0 mi/h
b: is the velocity of the wind = 15.0 mi/h
θ: is the angle between "a" and "b"
The angle between "a" and "b" can be found as follows:
[tex] \theta = 180.0 - 46.0 = 134.0 ^{\circ} [/tex]
Now, by using the law of cosines we have:
[tex] c^{2} = (75.0)^{2} + (15.0)^{2} - 2*75.0*15.0*cos(134.0) = 7413.0 [/tex]
[tex] c = 86.1 mi/h [/tex]
Therefore, the resultant velocity is 86.1 mi/h.
The law of sines is:
[tex] \frac{a}{sin(\gamma)} = \frac{b}{sin(\alpha)} = \frac{c}{sin(\theta)} [/tex]
Where:
γ: is the angle between "b" and "c"
α: is the angle between "a" and "c"
So, if we want to find "c" by using the law of sines, we need to know another angle besides θ (γ or α), and the statement does not give us.
I hope it helps you!
