Answer:
<em>The angle between their paths when they started is 93°.</em>
Step-by-step explanation:
<u>The Law of Cosines</u>
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:
When the two ships travel in different directions from the same point in the plane, they form an angle we called x in the image below.
Tyler's ship sails a=35 miles and Noah's ship sails for b=42 miles. At some time they are c=56 miles apart.
Since we know the values of all three side lengths, we solve the equation for x:
Substituting values:
Calculating:
Computing the inverse cosine:
The angle between their paths when they started is 93°.
