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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblem 2.5.2
Chapter 3, Problem 2.5.2

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II.
I. S 70° W


II. 1. A. B. C. 2. S 70° W 3. 4. D. E. F. 5. 6. 7. G. H. 8. 9. 10. I. J.

Verified step by step guidance
1
Understand that a bearing is a way to describe direction using degrees measured clockwise from the north line. Bearings are typically given in the format: N or S followed by an angle and then E or W (e.g., S 70° W).
Interpret the bearing S 70° W: start facing due south (180°), then rotate 70° towards the west. This means the direction is 70° west of south.
Convert the bearing into a standard angle measured counterclockwise from the positive x-axis (east) if needed, or visualize it on a compass rose to match it with the correct graph.
Look at each graph in Column II and identify which one shows a vector or line pointing 70° west of south. This involves checking the orientation of the line relative to the cardinal directions shown.
Match the bearing S 70° W with the graph that correctly represents this direction, ensuring the angle and quadrant correspond to the bearing's description.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding Bearings

Bearings are a way to describe direction using degrees measured clockwise from the north line. A bearing like S 70° W means starting from the south, rotate 70 degrees towards the west. This system helps in navigation and plotting directions on a map or graph.
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Example 2

Interpreting Compass Directions

Compass directions combine cardinal points (N, S, E, W) with angles to specify precise directions. For example, S 70° W indicates a direction 70 degrees west of due south. Understanding how to translate these into angles on a coordinate plane is essential for matching bearings to graphs.
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Finding Direction of a Vector

Graphical Representation of Directions

Graphs or diagrams often depict directions as vectors or lines from a reference point. Matching a bearing to a graph requires visualizing or drawing the angle relative to north or south, then identifying the correct graph that corresponds to the given bearing.
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Finding Direction of a Vector Example 1
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Use a calculator to evaluate each expression. 2 sin 25°13' cos 25°13' - sin 50°26'

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CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.


Column I: 1.

csc⁻¹ 4

Column II:

A. 88.09084757°

B. 63.25631605°

C. 1.909152433°

D. 17.45760312°

E. 0.2867453858

F. 1.962610506

G. 14.47751219°

H. 1.015426612

I. 1.051462224

J. 0.9925461516

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Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods. (-4, 0)

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