Filiz is walking at a bearing of 300°. When she has traveled 20 meters, how far west from her starting point is she? Round to the nearest tenth
To determine how far west Filiz is from her starting point, we need to use trigonometry.
Step 1: Draw a diagram to visualize the problem.
Let's assume that Filiz's starting point is the origin (0,0). We can represent her starting point as (0,0) on a coordinate plane.
Step 2: Determine the angle and distance traveled.
The bearing of 300° means that Filiz is walking in a direction that is 300 degrees counterclockwise from due east.
Since she has traveled 20 meters, we can represent this distance as R = 20 on our coordinate plane.
Step 3: Convert the bearing into an angle relative to the positive x-axis.
Since the bearing is measured counterclockwise from due east, we need to subtract it from 360 degrees to get the angle relative to the positive x-axis.
360° - 300° = 60°
So, Filiz is walking at an angle of 60 degrees relative to the positive x-axis.
Step 4: Use trigonometry to find the x-coordinate (distance west).
To find how far west Filiz is, we need to find the adjacent side length using trigonometry.
Recall that in a right-angled triangle, the cosine of an angle is equal to the adjacent side divided by the hypotenuse.
In this case, the adjacent side is the x-coordinate (distance west), and the hypotenuse is the distance traveled (R = 20).
cos(60°) = adjacent / 20
Adjacent = cos(60°) * 20
Step 5: Calculate the distance west.
Using a calculator or trigonometric table, we find that cos(60°) is 0.5.
Adjacent = 0.5 * 20 = 10
So, Filiz is approximately 10 meters west from her starting point.