How much farther must she fly to get to Indianapolis?

Question

A pilot intends to fly a distance of 175 miles from Chicago to Indianapolis.  She begins 21 degrees off her course and proceeds 70 miles before discovering her error.  After correcting her course, how much farther must she fly to get to Indianapolis?

Answer 1

1. let's use the law of cosines for this :)

2. let a = 70 and b = 175

3. also, 21° is the angle that is opposite to the side of the triangle that we are looking for

4. the law of cosines = c² = a² + b² - 2*a*b*cos(21°)

5. substitute the values in: c² = (70)² + (175)² - 2*70*175*cos(21°)

6. c² ≈ 12652.280

7. c ≈ ±√12652.280 ≈ ±112.482

8. since we're dealing with the magnitude of a displacement vector, we take the absolute value of ±112.482, which is 112.482

9. therefore, she must fly ≈ 112 miles farther in order to reach Indianapolis