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.

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.

Let's consider types of triangles with the three cases of given information shown below.

SASYou may have a side, an angle, and then another side

AAAYou may have all three angles.

SSSYou 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

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 Cusing 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

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

Cabbac cos2222 The Law

of Cosines

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 cos2222

LAW OF COSINES

Cabbac cos2222

Baccab cos2222

Abccba cos2222

LAW OF COSINES

abcbaC

2cos

222

acbcaB

2cos

222

bcacbA

2cos

222

Use these to findmissing sides

Use these to find missing angles

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)

Solve a triangle where b = 1, c = 3 and A = 80°

80B

C

a 1

3

This is SAS

Abccba cos2222 times the cosine of the angle between

those sides

One side squared

2a

sum of the square of the other sides

minus 2 times the productof those

other sides 312 80cos22 31

a = 2.99

A

We'll label the side that we found.

80

2.99 1

3

sin80 sin2.99 3

3sin802.99

81.2

18.8B

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.

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.

     

HomeworkDirection: Find the missing part of the given oblique triangles using law of cosine.

1. 2.