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

CSIN

c

BSIN

b

ASIN

a

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

c

CSIN

b

BSIN

a

ASIN

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

CSIN

c

BSIN

b

ASIN

a

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

CSIN

c

BSIN

b

ASIN

a

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

CSINSINASIN

a

1.37

44

5.29

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

9.60

8737.05.29

7734.25

5.29

))(5.29(

7734.25))(5.29(

)1.37)(6947.0())(5.29(

1.37

6947.0

5.29

1.37

44

5.29

C

CSIN

CSIN

CSIN

CSINCSIN

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

ZSIN

z

YSIN

y

XSIN

x

*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

ZSIN

z

YSIN

y

XSIN

x

*Found missing angle by using 180° rule

25

3

6788 SINSIN

y

SIN

x

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

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

25

3

88 SINSIN

x

25

3

67 SINSIN

y

and

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

1.74226.0

9982.2

4226.0

4226.0

9982.24226.0

)3)(9994.0(4226.04226.0

3

9994.0

25

3

88

x

x

x

x

xSINSIN

x

5.64226.0

7615.2

4226.0

4226.0

7615.24226.0

)3)(9205.0(4226.04226.0

3

9205.0

25

3

67

y

y

y

y

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

43

2.27

7265 SINSIN

b

SIN

a

*Found missing angle by using 180° rule

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

43

2.27

65 SINSIN

a

43

2.27

72 SINSIN

b

and

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

cma

aSINSIN

a

2.366820.0

24.7a

0.6820

0.6820

24.70.6820a

7.2)(0.9063)(20.6820a

multiply)-(cross 6820.0

2.27

9063.0

(replace) 43

2.27

65

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

cmb

bSINSIN

b

386820.0

25.9b

0.6820

0.6820

25.90.6820b

7.2)(0.9511)(20.6820b

multiply)-(cross 6820.0

2.27

9511.0

(replace) 43

2.27

72

Homework

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