Question

A ship travels 10 miles from Point A to Point B, makes a turn of 106 degrees, and travels 14 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

19.32 miles

Explanation:

AB =10 miles

∠ABC = 106°

BC = 14 miles

Now we are supposed to find AC

We will use cosine law

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

`AC^2=AB^2+BC^2-2(AB)(BC) cos 106^(\circ)`

`AC^2=100+196+77.1784596`

`AC^2=373.1784596`

`AC=√(373.1784596)`

`AC=19.31782`

Thus it will travel 19.32 miles on the last leg of the trip .

Answer 2

See the attached picture for the solution: