Question

Two ships set sail in different directions from the same place. Tyler's ship sails 35 miles, while Noah's ship sails for 42 miles. At the same time, they are 56 miles apart. What was the angle between their paths when they started?

A. 56 degrees
B. 45 degrees
C. 60 degrees
D. 30 degrees

Answer 1

To find the angle between the paths of the two ships, we can use the concept of vector addition. By creating a triangle with the given information and using the Law of Cosines, we can find that the angle between their paths is approximately 82.7 degrees.

Step-by-step explanation:

To find the angle between the paths of the two ships, we can use the concept of vector addition. Let's assume that the starting point of both ships is the origin. Tyler's ship travels 35 miles in one direction and Noah's ship travels 42 miles in the opposite direction. Since they are 56 miles apart, we can create a triangle with sides of 35 miles, 42 miles, and 56 miles.

Using the Law of Cosines, which states that c^2 = a^2 + b^2 - 2abcos(C), where c is the side opposite angle C, a and b are the lengths of the other two sides, and C is the angle opposite side c, we can solve for the angle between their paths:

56^2 = 35^2 + 42^2 - 2 * 35 * 42 * cos(C)

Cos(C) = (35^2 + 42^2 - 56^2) / (2 * 35 * 42)

Cos(C) = 0.1143

C = arccos(0.1143)

C ≈ 82.7 degrees

Therefore, the angle between their paths when they started is approximately 82.7 degrees.