NWACC Dept of Mathematics
Dept Final Exam Review for Trig - Part 3
Trigonometry, 9th Edition
;
Lial, Hornsby, Schneider
Fall 2008
1
Departmental Final Exam Review for Trigonometry
Part 3: Chapters 7 and 8
Departmental Objectives
:
7.
Defining, using, and applying the Law of Sines and the Law of Cosines.
[Sections: 7.1, 7.2, 7.3]
8.
Performing operations with and applying vectors.
[Sections: 7.4, 7.5]
9.
Converting complex numbers into trigonometric form & vice versa, performing operations with complex numbers,
and finding roots and powers of complex numbers.
[Sections: 8.1, 8.2, 8.3, 8.4]
10.
Converting between rectangular & polar coordinates and graphing polar coordinates and equations.
[Section: 8.5]
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