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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.

 Mar 23, 2020
 #1
avatar+21017 
+1

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.

 Mar 23, 2020
 #3
avatar+111330 
+1

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 :

 

 

cool cool cool

 Mar 23, 2020
 #4
avatar+23710 
+2

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

 Mar 23, 2020

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