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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 2.5.8
Chapter 3, Problem 2.5.8

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II.
I. 8. 270°


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

Verified step by step guidance
1
Step 1: Understand what a bearing is. A bearing is a direction measured clockwise from the north line. It is usually expressed in degrees from 0° to 360°, where 0° or 360° represents north, 90° east, 180° south, and 270° west.
Step 2: Identify the bearing given in the problem, such as 270°, and recall that this corresponds to a direction exactly west.
Step 3: For each bearing in Column I, visualize or sketch the direction starting from the north and rotating clockwise by the given degree measure.
Step 4: Examine each graph in Column II and determine which one matches the direction indicated by the bearing. For example, a bearing of 270° should point directly to the left (west) on the graph.
Step 5: Match each bearing from Column I with the graph in Column II that correctly represents the direction of that bearing, ensuring the clockwise measurement from north aligns with the graph's direction.

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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 express direction using degrees measured clockwise from the north direction (0° or 360°). They are commonly used in navigation and surveying to specify precise directions, typically ranging from 0° to 360°. Recognizing how bearings correspond to compass directions is essential for matching them to graphical representations.
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Example 2

Interpreting Angular Measurements on Graphs

Graphs representing bearings often use angles drawn from a reference line, usually the vertical north line. Understanding how to read these angles on a graph, including clockwise rotation and quadrant placement, helps in correctly associating a bearing measure with its visual depiction.
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Graphing Intercepts

Relationship Between Bearings and Coordinate Axes

Bearings relate to the standard coordinate axes where north corresponds to 0° or 360°, east to 90°, south to 180°, and west to 270°. Knowing this relationship allows one to translate between bearing angles and their positions on Cartesian or polar coordinate graphs, facilitating accurate matching of bearings to graphs.
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Related Practice
Textbook Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

1/ sec 14.8°

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Textbook Question

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.

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Textbook Question

Find exact values of the six trigonometric functions for each angle A.

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Textbook Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

tan 421° 30'

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Textbook Question

(Modeling) Length of a Sag Curve When a highway goes downhill and then uphill, it has a sag curve. Sag curves are designed so that at night, headlights shine sufficiently far down the road to allow a safe stopping distance. See the figure. S and L are in feet. The minimum length L of a sag curve is determined by the height h of the car's headlights above the pavement, the downhill grade θ₁ < 0°, the uphill grade θ₂ > 0°, and the safe stopping distance S for a given speed limit. In addition, L is dependent on the vertical alignment of the headlights. Headlights are usually pointed upward at a slight angle α above the horizontal of the car. Using these quantities, for a 55 mph speed limit, L can be modeled by the formula (θ₂ - θ₁)S² L = ————————— , 200(h + S tan α) where S < L. (Data from Mannering, F., and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.) Compute length L, to the nearest foot, if h = 1.9 ft, α = 0.9°, θ₁ = -3°, θ₂ = 4°, and S = 336 ft.

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Textbook Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. csc 145° 45'

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