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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 2.5.10
Capitolo 3, Problema 2.5.10

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.

Guida verificata passo dopo passo
1
Understand that a bearing is a way to describe direction using angles measured clockwise from the north line. For example, the bearing 'N 70° E' means starting from the north, rotate 70 degrees towards the east.
Recall that bearings are always measured clockwise from the north direction, so 'N 70° E' corresponds to an angle of 70 degrees east of north.
To match the bearing with the correct graph, visualize or draw the angle starting from the vertical north line and rotating 70 degrees towards the right (east).
Look at each graph in Column II and identify which one shows a vector or line starting from north and rotated 70 degrees towards the east direction.
Select the graph that correctly represents this angle, ensuring the direction matches the bearing 'N 70° E' as described.

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Understanding Bearings

Bearings are a way to describe direction using angles measured clockwise from the north line. They are typically expressed in three parts: a starting cardinal direction (N or S), an angle less than 90°, and an ending cardinal direction (E or W). For example, N 70° E means starting from north, rotate 70° towards the east.
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Percorso guidato
3:22
Example 2

Interpreting Directional Angles on Graphs

Graphs representing bearings usually show vectors or lines originating from a point, indicating direction. Understanding how to translate a bearing like N 70° E into a graphical angle involves visualizing the angle relative to the north axis and correctly identifying the quadrant or direction on the graph.
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05:13
Finding Direction of a Vector

Matching Bearings to Visual Representations

Matching bearings to graphs requires recognizing the angle's orientation and direction on the coordinate plane. This involves comparing the given bearing angle with the angle shown in the graph, ensuring the correct quadrant and direction (e.g., northeast, southwest) are matched accurately.
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Percorso guidato
5:25
Introduction to Transformations
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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.

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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:

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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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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(Modeling) Grade Resistance Solve each problem. See Example 3. Find the grade resistance, to the nearest ten pounds, for a 2400-lb car traveling on a -2.4° downhill grade.

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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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