SOLUTION: In tracking the relative location of two aircraft, a controller determines that the distance from the control tower to the first aircraft is 140 miles and the distance to the secon

Algebra ->  Trigonometry-basics -> SOLUTION: In tracking the relative location of two aircraft, a controller determines that the distance from the control tower to the first aircraft is 140 miles and the distance to the secon      Log On


   

Question 866265: In tracking the relative location of two aircraft, a controller determines that the distance from the control tower to the first aircraft is 140 miles and the distance to the second is 70 miles. The angle between the two aircraft is 40°. How far apart are they? (Round your answer to one decimal place.)
The answer unit is in miles...?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This is NOT drawn to scale:

The control tower is point S, and distances to each plane is shown and labeled. The angle at the point S between the two planes is 40 degrees.

You want the length, c which you will find using Law Of Cosines.
Fitting directly into the formula,
140%5E2%2B70%5E2-2%2A140%2A70%2Acos%2840%29=c%5E2
highlight%28c=sqrt%28140%5E2%2B70%5E2-2%2A140%2A70%2Acos%2840%29%29%29
and computations are yours to finish.