Post on 22-Feb-2016
description
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