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Integrated Math 4
Day 56
14.4 Law of Cosines (Supplement)
[not in the book]

Daily Openers

Go over and collect homework
14.4 Law of Cosines
 Solving a  means finding all 3 angle measures and all 3 side lengths.
solving a triangle – finding all the angle measures and side lengths of a triangle.
 To solve a Right Triangle → use trigonometric functions
oblique triangle – triangles that have no right angles.
 To solve an oblique triangle → you need to know a side and at least 2 other parts
 A-A-S, A-S-A, and S-S-A can be solved using the Law of Sines
Review
Ex. Solve the triangle.
a = 8 inches
b = 19 inches
c = 14 inches
 What is problem in solving the above triangle?
 S-S-S and S-A-S are cases where Law of Sines does not work.
 In those two cases use Law of Cosines.
LAW OF COSINES
Let ABC be a triangle with sides a, b, and c, then:
Standard Form
a 2  b 2  c 2  2bc cos A
b 2  a 2  c 2  2ac cos B
c 2  a 2  b 2  2ab cos C
Alternative Form
b2  c2  a2
cos A 
2bc
2
a  c2  b2
cos B 
2ac
2
a  b2  c2
cos C 
2ab
Ex. Solve the triangle.
a = 55, b = 50, c = 90
Ex. Solve the triangle.
B = 50˚, a = 15, c = 20
Ex. Solve the triangle.
x = 20, y = 22, z = 18
Ex. Solve the triangle.
L = 32˚, m = 8, n = 7
Ex. Solve the triangle.
d = 60, e = 22, f = 55
Ex. Solve the triangle.
D = 45˚, e = 10, f = 5
Ex. Solve the triangle.
a = 17, b = 16, c = 8
Ex. Solve the triangle.
C = 40˚, a = 110, b = 100
Hero’s Area Formula
The area of a triangle with sides of length a, b, and c is
Area  ss  a s  bs  c  ,
1
where s  a  b  c 
2
Ex. Find the area of a triangle with a = 25 cm, b = 60 cm, and c = 45 cm
Ex. Find the area of a triangle with a = 100 m, b = 55 m, and c = 61 m
Ex. Find the area of a triangle with a = 12 in, b = 9 in, and c = 5 in
Homework – Worksheet 14.4
Daily Openers – 1. Use a calculator to find the ratio: sin 40
2.–3. Find the sin H, cos H, and tan J:
4. Find the mM:
5. Find y.