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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 2.5.5
Chapter 3, Problem 2.5.5

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


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

Verified step by step guidance
1
Understand that a bearing is a direction measured clockwise from the north line. For example, a bearing of N 70° W means starting from north, rotate 70° towards the west.
Convert the given bearing into a standard angle measured counterclockwise from the positive x-axis (east direction) if needed, or visualize it on a compass rose to match with the graphs.
For each bearing in Column I, identify the quadrant or direction it points to by interpreting the notation (e.g., N 70° W lies in the northwest quadrant).
Examine each graph in Column II and determine which direction or angle it represents, comparing it with the bearing's direction from Column I.
Match each bearing from Column I with the graph in Column II that correctly represents the same direction, ensuring the angle and quadrant correspond.

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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. A bearing like N 70° W means starting at north, rotate 70 degrees towards the west. This system helps in navigation and mapping by providing precise directional information.
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Example 2

Interpreting Directional Notation

Directional notation such as N 70° W combines cardinal points with angles to specify a direction. It indicates the angle from the north towards the west, rather than from the east or south, which is crucial for correctly matching bearings to their graphical representations.
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i & j Notation

Graphical Representation of Bearings

Graphs or diagrams representing bearings show directions as angles from the north line, often with arrows or lines. Understanding how to translate a bearing into a visual angle on a graph is essential for matching given bearings to their correct graphical depiction.
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Finding Direction of a Vector Example 1
Related Practice
Textbook Question

(Modeling) Grade Resistance Solve each problem. See Example 3. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds.

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Textbook Question

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

Column I:

cos⁻¹ 0.45

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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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

csc θ = 1.3861147

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Textbook Question

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

sec θ = 1.1606249

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Textbook Question

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. ½ sin 40° = sin [½ (40°)]

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Textbook Question

Solve each problem. See Examples 1 and 2. Flying Distance The bearing from A to C is N 64° W. The bearing from A to B is S 82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C.

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