Spirit to Working

SINE LAW, COSINE LAW, TRIANGLE AREA

Competence Standard

5. Using the ratios, functions, equation and identities of trigonometry to problem

solving

Basic Competence

5.2 Planing mathematical model of problem which interlaced with comparison ,

function, equation and identities trigonometric.(C5)

)

Indicator

1. Solving calculation problem using sinus and cosinus formulates. (C5)

2. Calculating area triangle which the component are given.(C3)

Prerequisite

SINE LAW

Spirit to Working

COSINE LAW

Instruction

DISCUSS WITH YOUR PAIR

ATTENTION YOUR TEACHER PROPERLY

Spirit to Working

FINDING ANGLE USING SINE RULE

Consider the Sine Law again

We are going to change the subject of the formula to , , and

Follow the following step

Write down the sine law again

....................... = ........................

....................... =

Write down the sine law again

....................... = ........................

....................... =

Write down the sine law again

....................... = ........................

....................... =

Now cross multiply

or

Spirit to Working

FINDING ANGLE USING COSINE RULE

Consider the Cosine Law again

a2 = b2 + c2 – 2bcCosA

b2 = a2 + c2 – 2acCosB

c2 = a2 + b2 – 2abCosC

We are going to change the subject of the formula to

Follow the following step

Write down the sine law again

a2 = b2 + c2 – 2bcCosA Turn the formula around

.................................. = ..................... Take b2 and c2 across

b2 = a2 + c2 – 2acCosB Turn the formula around

.................................. = ..................... Take b2 and c2 across

Divide by – 2 bc.

Divide top and bottom by -1

You now have a formula for finding an angle if you know all

three sides of the triangle.

Divide by – 2 bc.

Divide top and bottom by -1

You now have a formula for finding an angle if you know all

three sides of the triangle.

Spirit to Working

c2 = a2 + b2 – 2abCosC Turn the formula around

.................................. = ..................... Take b2 and c2 across

TRIANGLE AREA

Given a triangle ABC

Area of beside triangle ABC is :

L = ½ x AB x CD (1)

At the triangle ABC we make altitude CD.

Consider triangle ADC, right in D applied

CD= ........ x ........ (2)

From (1) and (2) obtained relation as follows

L = ½ x .... x CD

L = ½ x ..... x ...... . .........

L = ½ x ........ . ......... . ..........

Area of beside triangle ABC is :

L = ½ x AB x CD (1)

At the triangle ABC we make altitude CD.

Divide by – 2 bc.

Divide top and bottom by -1

You now have a formula for finding an angle if you know all

three sides of the triangle.

Spirit to Working

Consider triangle BDC, right in D

applied

CD= ........ x ........ (2)

From (1) and (2) obtained relation as

follows

L = ½ x .... x CD

L = ½ x ..... x ...... . ........

L = ½ x ........ . ......... . ..........

Area of beside triangle ABC is :

L = ½ x AC x BE (1)

At the triangle ABC we make altitude

BE.

Consider triangle BEC, right in E applied

BE = ........ x ........ (2)

From (1) and (2) obtained relation as

follows

L = ½ x .... x BE

L = ½ x ..... x ...... . ........

L = ½ x ........ . ......... . ..........

CONCLUSION (drawing conclusion with your own words)

.......................................................................................................................................................

.......................................................................................................................................................

.......................................................................................................................................................

.......................................................................................................................................................

.......................................................................................................................................................

.......................................................................................................................................................

Spirit to Working