The Law of Cosines demo

The Law of Cosines demo- for demonstration teaching
4A's

2. The Fast and the
Furious
- is a group battle wherein
every group will select at
least one representative to
perform the given task
using the graphing board.

3. Tasks
•Write the formula in law of sines..
•Enumerate the cases wherein we use the
law of sine in finding the missing parts of
oblique triangles.
•List down the cases wherein we cannot use
the law of sine in finding the missing parts
of oblique triangles.

4. Let's consider types of triangles with the three cases of
given information shown below.
SAS
You may have a side, an
angle, and then another
side
AAA
You may have all three angles.
SSS
You may have all three
sides
This case doesn't determine a
triangle because similar
triangles have the same
angles and shape but "blown
up" or "shrunk down"
AAA

5. Activity
Direction: Follow the procedures and answer the questions that follow.
•Draw triangle ABC on the rectangular coordinate plane.
•From B, draw its altitude, then find the trigonometric ratio of C
using cos and sin as illustrated below.
•Using your answer in letter b, find value of x and y
•Find the coordinates of A and B.
•Use the distance formula in finding the measure of side c (use two
points of the line)
a
b
c
(b, 0)
y
x A
B(x, y)
C

6. Questions
•How did you solve for cos C and sin C?
•What is the formula formed?
•If the new formula is known as the law of cosine,
then differentiate law of cosine from law of sine

7. Cabbac cos2
222
-+=
The Law of
Cosines

8. Law of Cosine
•The square of the length of one side is equal
to the sum of the square of the other two
sides minus the product of twice the two
sides and the cosine of the angle between
them.
Cabbac cos2
222
-+=

9. LAW OF COSINES
Cabbac cos2
222
-+=
Baccab cos2
222
-+=
Abccba cos2
222
-+=
LAW OF COSINES
ab
cba
C
2
cos
222
-+
=
ac
bca
B
2
cos
222
-+
=
bc
acb
A
2
cos
222
-+
=
Use these to find
missing sides
Use these to find
missing angles

10. We used the Law of Sines in finding the missing
parts of the given oblique triangles if the:
•Two angles and one side are given (AAS and
ASA case)
•Two sides and an angle opposite one of the
sides are given ( SSA case)

Otherwise, we use the Law of Cosines if:
•Two sides and one included angle are known
(SAS case)
•Three sides are known ( SSS case)

11. Solve a triangle where b = 1, c = 3 and A = 80°
80
B
C
a
1
3
This is SAS
Abccba cos2
222
-+=
times the
cosine of
the angle
between
those
sides
One side squared
2
a
sum of the
square of the
other sides
minus 2
times the
product
of those
other
sides
()()312- 80cos
22
31+=
a = 2.99
A

12. We'll label the side that we found.
80
2.99
1
3
sin80 sin
2.99 3
g
=
3sin80
2.99
g=
81.2
18.8
B
C
A
c
Sin c
B= 180 – (m A + m C)
∠ ∠
B= 180 – (80 + 81.2) = 18.8
= 81.2
Hint: We have an angle and
a side opposite it.

13. Quiz no. 12 (this can be done by pairs)
Direction: Apply the law of cosine to find the all missing parts of
the given oblique triangle.
1. 2. 3.

14. Homework
Direction: Find the missing part of the given oblique
triangles using law of cosine.
1. 2.