A hiker travels at 2.8 miles per hour at a heading of N49°W from a ranger station. After 4 hours, how far north and how far west is the hike from the ranger station?

Step-by-step explanation:

The diagram showing the pictorial view is attached below.

From the image, the distance of the hiker traveled which is denoted by "h" can be determined as follows:

h = 2.8 mi/hr × 4 hr

h = 11.2 mi

Using the trigonometric function;

The distance of how  far North is the hike from the ranger station can be determined by using the function of Sin θ

x = Sin 41 (11.2)

x = 0.6561(11.2)

x = 7.34832

x ≅ 7.35 miles

The distance of how far west the hike from the ranger station is calculated by using:

y = 0.7547 × (11.2)

y = 8.45 miles

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