How far is she from her starting position?

Question

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 670 mi/h, how far is she from her starting position?

Answer 1

1.5(670) = 1005 miles straight

then 2(670) = 1340 miles 10 degrees

use the law of cosines

c^2 = a^2 + b^2 -2abCosC

c^2 = 1005^2 + 1340^2 - (1005)(1340)Cos170

= 1010025 + 1795600 - 1346700(-9848

= 1010025 + 1795600 + 1326240.6

c^2 = 4131865.6

c = 2,032.7 = distance from the starting place

it had to be less than 1005+1340 = 2345