Question

A cruise ship travels 330 miles due east before turning 25 degrees north of east. It travels 180 miles along its new course. How far is the cruise ship from its initial position?

Answer 1

Hence, the distance of the ship from initial position is:

498.977 miles.

Explanation:

We will apply the cosine law to calculate the distance of the cruise ship from the initial position.

The cosine law is given as:

`c^2=a^2+b^2-2ab\cos C`

where a is the distance covered by the ship in east direction.

b is the distance covered by ship in the north-east direction.

and c is the distance of the ship from the initial point.

The angle C is the angle between a and b and is given by:

C=155°.

Here we have: a=330 miles, b=180 miles.

Hence, we apply the cosine law to obtain:

`c^2=(330)^2+(180)^2-2* 330* 180* \cos 155\\\\c^2=108900+32400-118800* (-0.906308)\\\\c^2=248977.944\\\\c=498.977`

Hence, the distance of the ship from initial position is:

498.977 miles.

Answer 2

we know that
applying the law of cosines
c²=a²+b²-2*a*b*cos C

in this problem
a=330 miles
b=180 miles
c=-----> distance of the cruise ship from its initial position
C=180-25----> C=155°

see the attached picture to better understand the problem
c²=a²+b²-2*a*b*cos C----> c²=330²+180²-2*330*180*cos 155
c²=248969.37------> c=498.97 miles

the answer is
498.97 miles