Chapter 6 Investigating Non-Right Triangles as Models for Problems:

6.3 Investigating the Sine Law

6.3 Investigating the Sine Law

Goals for Today:• Learn one of the ways that we can find

unknown sides and angles in a non-right angle triangle

6.3 Investigating the Sine Law

Minds On:• Sine Law Investigation textbook p.546• I will handout graph paper and protractors• What conclusion do you draw?

6.3 Investigating the Sine Law

• If we have a non-right angle triangle, we can’t use the primary trig ratios to find an unknown side or angle

• In this case*, we can use the Sine Law to solve for an unknown angle or side if we are given:

• 2 sides and one angle across from a known side, or

• 2 angles and any side• *The Sine law will work in right angle triangles

6.3 Investigating the Sine Law

• The Sine Law is: use this if solving for a side

CSINc

BSINb

ASINa

The small letters represent sidesThe large letters represent anglesYou work with two out of the three ratios

6.3 Investigating the Sine Law

• The Sine Law is also: use this if solving for

cCSIN

bBSIN

aASIN

The small letters represent sidesThe large letters represent anglesYou work with two out of the three ratios

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

A

C

B

29.5cm

44°

37.1cm

Ex. 1 Find angle C

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

A

C

B

29.5cm

44°

37.1cm

Ex. 1 Find angle C

Angle B is across from a known side...

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

Ex. 1. Find angle C in triangle ABC

CSINc

BSINb

ASINa

As with similar triangles, we need 3 out of 4 to be able to find the missing side or angle

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

Ex. 1. Find angle C in triangle ABC

CSINc

BSINb

ASINa

As with similar triangles, we need 3 out of 4 to be able to find the missing side or angle

CSINSINASINa

1.37

445.29

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

9.608737.0

5.297734.25

5.29))(5.29(

7734.25))(5.29()1.37)(6947.0())(5.29(

1.376947.0

5.29

1.37445.29

CCSIN

CSINCSINCSINCSIN

CSINSIN

Humour Break

6.3 Investigating the Sine Law – Given 2 Angles and any Side

X

ZY

z=3 cm y

x

88°

25°

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

Ex. 2. Find side x and find side y in triangle XYZ

ZSINz

YSINy

XSINx

*Found missing angle by using 180° rule

6.3 Investigating the Sine Law – Given 2 Sides and an Angle Across from a Known Side

Ex. 2. Find side x and find side y in triangle XYZ

ZSINz

YSINy

XSINx

*Found missing angle by using 180° rule

253

6788 SINSINy

SINx

6.3 Investigating the Sine Law – Given 2 Angles and any Side

6.3 Investigating the Sine Law – Given 2 Angles and any Side

253

88 SINSINx

253

67 SINSINy

and

6.3 Investigating the Sine Law – Given 2 Angles and any Side

1.74226.09982.2

4226.04226.0

9982.24226.0)3)(9994.0(4226.0

4226.03

9994.0

253

88

x

x

xx

xSINSIN

x

5.64226.07615.2

4226.04226.0

7615.24226.0)3)(9205.0(4226.0

4226.03

9205.0

253

67

y

y

yy

ySINSIN

y

6.3 Investigating the Sine Law – Given 2 Angles and Any Side

A

C

B

b

72°

43°27.2cm

a

Ex. 3 Find the length side a and side b

6.3 Investigating the Sine Law – Given 2 Angles and any Side

Ex. 1. Find side a and find side b in triangle ABC

6.3 Investigating the Sine Law – Given 2 Angles and any Side

Ex. 1. Find side a and find side b in triangle ABC

432.27

7265 SINSINb

SINa

*Found missing angle by using 180° rule

6.3 Investigating the Sine Law – Given 2 Angles and any Side

432.27

65 SINSINa

432.27

72 SINSINb

and

6.3 Investigating the Sine Law – Given 2 Angles and any Side

cma

aSINSIN

a

2.366820.024.7a

0.68200.6820

24.70.6820a7.2)(0.9063)(20.6820a

multiply)-(cross 6820.0

2.279063.0

(replace) 432.27

65

6.3 Investigating the Sine Law – Given 2 Angles and any Side

cmb

bSINSIN

b

386820.025.9b

0.68200.6820

25.90.6820b7.2)(0.9511)(20.6820b

multiply)-(cross 6820.0

2.279511.0

(replace) 432.27

72

Homework

• Monday, January 6th - Hwk p.549, #1-4, 6-10, 14 & 15