algebra 2 high school

Question

A ship travels west 103 miles. It then travels north 56 miles and ends up 126 miles from original position. How many degrees did it turn when it changed direction. Round to nearest tenth

Answer 1

It forms a triangle suppose ABC

side 1= AB=103 mile

side 2 = BC=56 mile

side 3=CA=126 miles

 

It changes direction 2 times

1. west tp norrh      =  angle b

2.north to original position =angle c

 

 

using law of cosine

 

AC² = AB² + BC² -2.AB.BC cos b

 

126² = 103² + 56² - 2(103)(56)cos b

 15876 =10609 +3136 - 11536 cos b

 

2131 = -11536 cos b

 

2131/-11536 = cosb

 

b =100.65

 

 

AB²  = BC² + AC²  - 2.BC.AC cos c

 

103² =56² + 126² -2*56*126 cos c

 

10609 =3136 +15876 - 14112 cos c

 

-8403 = -14112 cos c

 

0.5954 = cos c

 

c= 53.45

 

so first(west to north) it turn through  100.65 degree then it turns north to original position 53.45 degrees