precalc homework

Question

In tracking the relative location of two aircraft, a controller determines that the distance from the control tower to the first aircraft is 130 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.

Answer 1

 

Hi Emi,

 

This is equivalent to find out the length of the rest of the sides

when the length of two sides are given along with the angle between those two.

 

From the cosing rule, which is a² = b² + c² - 2·b·c·cos(A)

 

     a = √(130² + 70² - 2·130·70·cos(40°))

 

        = 88.6

 

The distance between two aircrafts is 88.6 miles.