Question

The question I need is question #13. Please provide a step by step answer. Thank You

Answer 1

Answer:

Step-by-step explanation:

We have plane 1 flying SW for 4 hours at a rate of 415 mph.  The distance he covers using the d = rt formula for distance, is 415(4) = 160 miles.

We also have plane 2 flying directly east (along the x-axis) for 4 hours at 327 mph.  The distance he covers using the d = rt formula for distance, is 327(4) = 1308 miles.  The angle in between them at this point is 135 degrees, and what we need to find is the length of the vector connecting the 2 planes.  IF this was right triangle trig that distance would be the hypotenuse and we could solve for it using Pythagorean's Theorem.  BUT it is NOT a right triangle, so we have to find some other means with which to solve for that length.  We will use the Law of Cosines to do this.

$?^2=1660^2+1308^2-2(1660)(1308)cos(135)$ which simplifies a bit to

$?^2=2755600+1712864-(-3070653.624)$

If you add all of that together, you'll get

$?^2=7537117.624$  and you'll take the square root of that to get that the distance between the 2 planes after 4 hours is

2745 miles