Question

A ship travels 10 miles from Point A to Point B, makes a turn of 112, and travels 16 miles to Point C. If the ship travels directly from Point C back to Point A, how many miles will it travel on the last leg of the trip (from Point C to Point A)? Round your answer to the nearest tenth of a mile.

Answer 1

Law of cosines:

$b= \sqrt{a^{2} + c^{2} -2ac*cos 112$

Let AB = a and BC = c  and AC = b

b= $b = \sqrt{ 10^{2} + 16^{2} - 2(10)(16) * cos 112$

$b = \sqrt{100 + 256 - 320*0.4559$

$b = \sqrt{356 - 145.91$

$b = 22.4$