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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblema 2.5.5
Capitolo 3, Problema 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.

Guida verificata passo dopo passo
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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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
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Domanda del libro di testo

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

I. 10. N 70° E


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

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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.

cot(90°-4.72°)

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Solve each problem. See Examples 3 and 4. Distance through a Tunnel A tunnel is to be built from point A to point B. Both A and B are visible from C. If AC is 1.4923 mi and BC is 1.0837 mi, and if C is 90°, find the measures of angles A and B.

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Solve each problem. See Examples 3 and 4. The figure to the right indicates that the equation of a line passing through the point (a, 0) and making an angle θ with the x-axis is y = (tan θ) (x - a). Find an equation of the line passing through the point (5, 0) that makes an angle of 15° with the x-axis.

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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. tan² 72°25' + 1 = sec² 72°25'

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