Question

Use appropriate units and significant figures.  USE THE LAW OF COSINES AND LAW OF SINES.

Answer 1

Answer:

The resultant velocity is 86.1 mi/h.    

Explanation:

The law of cosines is given by:

$c^{2} = a^{2} + b^{2} - 2abcos(\theta)$

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:

$\theta = 180.0 - 46.0 = 134.0 ^{\circ}$

Now, by using the law of cosines we have:

$c^{2} = (75.0)^{2} + (15.0)^{2} - 2*75.0*15.0*cos(134.0) = 7413.0$

$c = 86.1 mi/h$    

Therefore, the resultant velocity is 86.1 mi/h.    

The law of sines is:

$\frac{a}{sin(\gamma)} = \frac{b}{sin(\alpha)} = \frac{c}{sin(\theta)}$

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!