Upload
loraine-newman
View
223
Download
2
Embed Size (px)
Citation preview
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
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
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
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