Trigonometry, 8th Ed; Lial, Hornsby, Schneider Trig Final Exam Review

Trigonometry, 8th ed; Lial, Hornsby, Schneider Trig Final Exam Review F07 OfBrien

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Trigonometry Final Exam Review: Chapters 7, 8, 9

Note: A portion of Exam 3 will cover Chapters 1 . 6, so be sure you rework problems from the first and second exams and

from the Exam 1 and Exam 2 Reviews.

Directions: Work these problems with no resources other than the departmental formula sheet and a graphing calculator.

Your book, notebook, homework, solutions manual, etc. should be closed. Read and carefully follow all

directions. Show all of your work on all problems. Anytime you are asked to perform a calculation

manually or to give an exact answer, you may not use a calculator.

Chapter 7: Applications of Trigonometry and Vectors

1. Determine the remaining sides and angles of the triangle ABC. Show all work and / or support your answer.

2. Determine the remaining sides and angles of the triangle ABC. Show all work and / or support your answer.

C = 71.83‹, B = 42.57‹, a = 2.614

3. A ship is sailing due north. At a certain point the bearing of a lighthouse 12.5 km distant is N 38.8‹ E. Later on, the

captain notices that the bearing of the lighthouse has become S 44.2‹ E. How far did the ship travel between the two

observations of the lighthouse? Show all work and / or support your answer.

4. Mark notices that the bearing of a tree on the opposite bank of a river flowing north is 115.45‹. Lisa is on the same

bank as Mark, but 428.3 m away. She notices that the bearing of the tree is 45.47‹. The two banks are parallel. What

is the distance across the river? Show all work and / or support your answer.

5. Find the area of the triangle ABC. Show all work and / or support your answer.

A = 30.50‹, b = 13.00 cm, C = 112.60‹

6. A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides

are 52.1 m and 21.3 m, and the angle between them is 42.2‹. What is the area of the triangular lot? Show all work and /

or support your answer.

7. Determine the number of triangles ABC possible with the given parts. Show all work and / or support your answer.

a) b = 60, a = 82, B = 100‹ b) a = 35, b = 30, A = 40‹ c) B = 54‹, c = 28, b = 23

8. Find the unknown angles in triangle ABC, if the triangle exists. Show all work and / or support your answer.

a) C = 41‹20', b = 25.9 m, c = 38.4 m b) B = 48.2‹, a = 890 cm, b = 697 cm

c) B = 74.3‹, a = 859 m, b = 783 m

9. Solve the triangle ABC, if possible. Show all work and / or support your answer.

C = 52.3‹, a = 32.5 yd, c = 59.8 yd

Trigonometry, 8th ed; Lial, Hornsby, Schneider Trig Final Exam Review F07 OfBrien

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10. Solve the triangle ABC, if possible. Show all work and / or support your answer.

A = 38‹40', a = 9.72 km, b = 11.8 km

11. Solve each triangle and then find the area of the triangle. Approximate values to the nearest tenth. Show all work

and / or support your answer.

a) b)

12. Solve each triangle and then find the area of the triangle. Show all work and / or support your answer.

a) C = 28.3‹, b = 5.71 in., a = 4.21 in. b) a = 189 yd, b = 214 yd, c = 325 yd

13. The sides of a parallelogram are 4.0 cm and 6.0 cm. One angle is 58‹ while another is 122‹. Find the lengths of the

diagonals of the parallelogram. Show all work and / or support your answer.

14. A weight is supported by cables attached to both ends of a balance beam,

as shown in the figure. What angles are formed between the beam and the

cables? Show all work and / or support your answer.

15. Using the vectors in the figure below, draw a sketch to represent:

a) c + d b) d . c c) 3c

16. Use the vectors in the adjacent figure to find a) a + b, b) a . b, c) . a.

Show all work and / or support your answer.

17. For vectors u and w with angle Į between them, sketch the resultant, u + w.

u = 8 , w = 12 , ƒÆ = 20‹

18. Find the magnitude and direction angle for vector v = 15, -8 . Show all work and / or support your answer.

19. Vector v has magnitude v = 15.4 and direction angle ƒ¿ = 27o30Œ . Find the horizontal (a) and vertical (b)

components of v. Show all work and / or support your answer.

Trigonometry, 8th ed; Lial, Hornsby, Schneider Trig Final Exam Review F07 OfBrien

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20. Write vector v in component form, a, b .

Show all work and / or support your answer.

21. Two forces act at a point in the plane. One is 19

newtons, the other is 32 newtons. The angle

between the forces is 118‹. Find the magnitude of the

resultant force. Show all work and / or support your answer.

22. Use the parallelogram rule to find the magnitude of the resultant force for

the two forces shown in the adjacent