Three ships, a, b, and c, are anchored in the atlantic ocean. the distance from a to b is 36.318 miles, from b to c is 37.674 miles, and from c to a is 11.164 miles. find the angle measurements of the triangle formed by the three ships.

Let us draw the triangle

here the sides a= 37.674 miles

b= 11.164 miles

c= 36.318 miles

Lets use the cosine rule to solve for the angles

( we cannot use the sine law since we do not have the measure of any of the angles)

The cosine law

Let us plug in the values

C = 74.48°

We can use the sine law to calculate the value of angle A

A=

A = 87.38°

Now we can easily find the third angle B by subtracting angle A and C from 180°

B = 180-161.86

B = 18.14°

Hence we have all the three angles ( attached figure)

is this part of a question or something