A plane flies due south for 600 miles. It turns and flies 250 miles, 35 degrees east of south. How far is the plane from its origin.
+23245 Hint --
1) draw a picture to help determine the number of degrees in the angle between the 600 mi flight and the 250 mi flight
2) use the Law of Cosines.
+128475 The included angle we are looking for = 180 - 35 = 145°
Using the Law of Cosines the distance, D, from the origin is
D = sqrt ( 600^2 + 250^2 - 2 (600 * 250) cos (145° ) ) ≈ 817.5 miles
Here's a pic :
+36916 Another method ( you can refer to Chris' diagram)
South components 600 + 250 cos 35 = 804.788 m
East component 250 sin 35 = 143.394
RESULTANT distance (use pythagorean theorem) sqrt ( 807.788^2 + 143.394^2 ) = 817 .46 miles from origin
