Answer:
454 miles.
Step-by-step explanation:
Refer the attached figure.
A cruise ship travels 310 miles due east i.e. AB = 310 miles
Now a cruise turns 20 degrees north of east .i.e.∠CBE = 20°
Using linear pair :Sum of angles = 180°
∠CBA+∠CBE=180°
∠CBA=180°-20° =160°
It travels 150 miles its new course i.e. BC= 150 miles.
Now we are supposed to find How far is the cruise ship from its initial position
Now using cosine rule: [tex]c = \sqrt{a^2+b^2-2abcos\theta}[/tex]
a =BC = 150 miles
b= Ab = 310 miles
c = AC
[tex]\theta = 160^{\circ}[/tex]
Substitute the values.
[tex]c = \sqrt{150^2+310^2-2\times 150 \times 310 cos160^{\circ}}[/tex]
[tex]c = 453.8 \sim 454[/tex]
Thus the cruise ship is 454 miles from its initial position.
