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3 years ago

6

A cruise ship travels 310 miles due east before turning 20 degrees north of east. it travels 150 miles its new course. how far i

s the cruise ship from its initial position
A)295 miles
B)274 miles
C)454miles
D)160 miles

2 answers:

Elina [12.6K]3 years ago

3 0

D^2=x^2+y^2

d^2=(310+150cos20)^2+(150sin20)^2

d^2=205991.41373309

d=453.86mi

So C. to the nearest mile.

anyanavicka [17]3 years ago

3 0

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: $c = \sqrt{a^2+b^2-2abcos\theta}$

a =BC = 150 miles

b= Ab = 310 miles

c = AC

$\theta = 160^{\circ}$

Substitute the values.

$c = \sqrt{150^2+310^2-2\times 150 \times 310 cos160^{\circ}}$

$c = 453.8 \sim 454$

Thus the cruise ship is 454 miles from its initial position.

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