Download = a + b 2 – 2abcos C There is more than one angle that could have a

PRE-CALCULUS
WS 322
NAME ___________________________________
PERIOD ____ DATE _______________________
FILL-IN THE BLANK WITH THE CORRECT QUADRANTS.
3)
and II.
The cosine ratio is positive in quadrant(s) I and IV
The tangent ratio is positive in quadrant(s) I and III.
4)
The cosecant ratio is positive in quadrant(s) I
5)
The secant ratio is positive in quadrant(s) I
1)
2)
The sine ratio is positive in quadrant(s) I
and II.
and IV.
6)
The cotangent ratio is positive in quadrant(s) I and III.
________________________________________________________________________
AFTER READING 7.1, ANSWER THE FOLLOWING:
2
= a2 + b2 – 2abcos C
7)
What is the Law of Cosines: c
8)
What is the Law of Sines:
9)
Which Law has an ambiguous case? Law
sin A sin B sin C


a
b
c
of Sines Why?
There is more than one angle that could have a given Sine.
10)
The really cool thing about these “Laws” is that they apply to oblique triangles.
What does this mean?
Non-right Triangles.
Find the missing sides, a, b, c and angles A, B, C (if possible). If there are two
solutions find both. You will need to sketch the triangle. Round angles to the
nearest degree and sides to the nearest tenth.
11 – 13) a = 18 in., b = 9 in., C = 27
side c ≈ 10.8 in, angle A ≈ 131 and angle B ≈ 22
14- 16) a = 5, b = 7, C = 110
A

28, B  42, c  9.9
17-19) A = 77, B = 42, c = 9
C = 61, a  10.0, b  6.9
20-22) B = 72, b = 13, c = 4
A = 91, C = 17, a  13.7,
23 – 25) a = 8.9 cm, c = 5.2 cm and C = 38
No Possible Triangle.
About 22.8 in2 26)
Find the area of the given Triangle. (Round to the nearest
tenth)
C
5.5 in.
49
A
B
11 in.
Solve the following for  if 0 < θ < 360. (Round your answers to the nearest degree)
27)
cos  = -1/2
120, 240
28)
tan  = 5.27
29)
79, 259
30) What type of angles are 90, 180, 270, etc? Quadrantal
csc  = 4.1
14, 166
Angles.
“If the word quit is part of your vocabulary, then the word finish is likely not.”
B.G. Jett