---
title: "A hiker starts at a trailhead and walks \\(3.0 \\text{ km}\\) due North. The hiker then turns and walks \\(5.0 \\text{ km}\\) in a direction \\(37^\\circ\\) South of East to reach a campsite. (Note: \\(\\sin 37^\\circ \\approx 0.60\\); \\(\\cos 37^\\circ \\approx 0.80\\)). What is the magnitude of the hiker’s total displacement from the trailhead to the campsite?"
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url: "https://nerd-notes.com/ubq/114056/"
date_modified: "2026-06-22T09:46:36+00:00"
---

# A hiker starts at a trailhead and walks \(3.0 \text{ km}\) due North. The hiker then turns and walks \(5.0 \text{ km}\) in a direction \(37^\circ\) South of East to reach a campsite. (Note: \(\sin 37^\circ \approx 0.60\); \(\cos 37^\circ \approx 0.80\)). What is the magnitude of the hiker’s total displacement from the trailhead to the campsite?

A hiker starts at a trailhead and walks \(3.0 \text{ km}\) due North. The hiker then turns and walks \(5.0 \text{ km}\) in a direction \(37^\circ\) South of East to reach a campsite. (Note: \(\sin 37^\circ \approx 0.60\); \(\cos 37^\circ \approx 0.80\)). What is the magnitude of the hiker's total displacement from the trailhead to the campsite?

![A coordinate system with the origin (0,0) labeled 'Trailhead'. A vector labeled '3.0 km' points from the origin straight up to point A on the y-axis. At point A, a dashed horizontal line extends to the right. A second vector labeled '5.0 km' points from point A down and to the right, making a 37-degree angle with the dashed horizontal line. This vector ends at a point labeled 'Campsite' which lies on the positive x-axis. A dashed vector labeled with a question mark represents the direct path from the Trailhead to the Campsite.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1782121596-uCjr2p.jpg)

- **A.** \(2.0 \text{ km}\)
- **B.** \(4.0 \text{ km}\)
- **C.** \(5.8 \text{ km}\)
- **D.** \(8.0 \text{ km}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/114056/*