Could someone explain to me how to work this? You can use random numbers. I would just like to know how to figure out the correct answer.

The geese fly 4.5 km due west, then turn toward the north by 50 ∘ and fly another 4.5 km. How far west are they of their initial position? What is the magnitude of their displacement?

Given:

Let variable "c" denote the first distance traveled to the west from the origin.

Let variable "b" denote the second distance traveled going up 50° to the north.

b = 4.5km

c = 4.5km

Ф = 50°

Solution/Steps:

1. Sketch the problem.

2. Connect the two lines. You will notice you had formed a triangle.

3. Notice how you have a side-angle-side (SAS) triangle. However, we don't know yet the angle between the two sides but we know that a horizontal line has an angle of 180° and we also know that in the second travel, the geese went up to 50° toward the north. The supplementary angle of 50° is 130° since it sums up to 180°.

180° - 50° = 130°.

Thus, the angle between the line is equal to 130°.

A = 130°

4. Since it is an SAS triangle, we use the formula:

a² = b² + c² - 2bcosA

We are looking for a which is the displacement in this case.

substituting,

a² = 4.5² + 4.5² - 2 (4.5) cos (130°)

a = 6.8km

The displacement is equal to 6.8km.