1. Chapter 2 Trigonometry 2.4 The Cosine Law
Explain why the sine law cannot be used to solve each triangle. A B
28°
37°
115° C J K L 70 40 45
There is no known side opposite a known angle.
There is no known angle opposite a known side. P Q R 15 E D
85° 20 25 F
There is no known angle and only one known side.
There is no known angle opposite a known side
Pre-Calculus 11

2. a2 = b2 + c2 -2bc cosA b2 = a2 + c2 -2ac cosB c2 = a2 + b2 -2ab cosC
Law of Cosines
a2 = b2
+ c2
-2bc
cosA
b2 = a2
+ c2
-2ac
cosB
c2 = a2
+ b2
-2ab
cosC
When should we use the Law of Cosine to solve a triangle?
SSS Given the measure of three sides.
SAS Given the measure of two sides and one angle not opposite a side.
Pre-Calculus 11

3. Proof for the Law of CosinesB C A a c
pythagorean h x D
b - x
sohcahtoa b
Pre-Calculus 11

4. b2 = a2 + c2 -2ac cosB a2 = b2 + c2 -2bc cosA a = 37.9 cm
SAS Applying the Law of Cosines (to the nearest 10th)
Determine the length of side b
b2 = a2 + c2 -2ac cosB
= (230)2 + (150)2 - 2(230)(150)cos430
b = m
Determine the length of side a
a2 = b2 + c2 -2bc cosA
= (61)2 + (43)2 - 2(61)(43)cos380
a = cm
Pre-Calculus 11

5. SSS Finding an Angle Using the Law of Cosines
(to the nearest degree)
Determine the measure of angle A.
a2 = b2 + c2 -2bc cosA
382 = (61)(43) cosA
= -2(61)(43) cosA
Pre-Calculus 11

6. SSS Finding an Angle Using the Law of Cosines
(to the nearest degree)
Given triangle DEF, find
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7. h Solving Two Triangles b2 = (95)2 + (200)2 - 2(95)(200)cos50
From the following information determine the height of the balloon from the ground (to the nearest tenth)
b2 = (95)2 + (200)2 - 2(95)(200)cos50
b2 ~
b = (we need length side b before we can calculate h)
← Sine Law h
h =
The balloon is m from the ground b
Pre-Calculus 11

8. Begin by using the method
Solving Triangles
When solving triangles, it is important to choose the most appropriate method. The choice depends on the given information. Place the letter of the appropriate method beside the given information.
Given Information
Begin by using the method
Three sides
Three angles
Two angles and any side
Right triangle
Two sides and the angle between them
Two sides and the angle opposite one of the sides
A. Primary trig ratio
SSS C
AAA D
B. sine law
AAS B
C. cosine law A
D. none of the above
SAS C
SSA B
Pre-Calculus 11

9. Assignment Suggested Questions
Page 119: (1-6)ac, 8, 10, 12, 14, 17, 19, 20, 23
Pre-Calculus 11