13.5 Law of Sines KJ.notebook
April 15, 2015
What are ways that we can solve right triangles?
What about nonright triangles?
1
13.5 Law of Sines KJ.notebook
April 15, 2015
Law of Sines For a triangle with angles of measures A, B, and C and sides of lengths a, b, and c, then
sinA sinB sinC = b = c a
B a
c A
b
C
2
13.5 Law of Sines KJ.notebook
Ex
April 15, 2015
Solve the triangle
C 350m
b 590
A
c
380
3
13.5 Law of Sines KJ.notebook
April 15, 2015
Think back one year ago when you were young, carefree and in Geometry....... Remember the triangle congruence shortcuts?
SSS SAS ASA AAS
SSA AAA
We can only use law of sines with a few of these cases. Which ones?
ASA
AAS
SSA
4
13.5 Law of Sines KJ.notebook
April 15, 2015
The ASA and AAS cases: No issues, nothing weird, just do the law of sines.
The SSA case: careful!
There are scenarios where the given information, gets you: • No triangle • 1 triangle • 2 triangles If the only angle given is acute...
If the only angle given is obtuse...
46°
92°
247
148
21
16
110
o
40
o
A
What type of angle is: Angle A? Angle A'?
What relationship do these two angles share?
5
13.5 Law of Sines KJ.notebook
April 15, 2015
State the case (AAS, ASA, or SSA), that apply to the given measurements on each triangle.
15
107
o
20
25o
11
115
11
45
o
12
o
6
13.5 Law of Sines KJ.notebook
April 15, 2015
Solve each possible triangle. o
Ex A = 40, a = 13, b = 16
o
Ex A = 51, a = 3.5, b = 5
Ex Two lifeguards are watching a windsurfer. The lifeguards are 300 feet away from each other on the beach. They both see the windsurfer fall and are concerned. Larry notices there is a 40 degree angle between the windsurfer and Lance (the other lifeguard). Lance notices there is a 45 degree angle between Larry and the windsurfer. Which lifeguard is closer to the windsurfer?
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13.5 Law of Sines KJ.notebook
April 15, 2015
Area of a Triangle when a height is unknown
B c
A 1 Area = bc sin A 2
a
b 1 Area = ac sin B 2
C 1 Area = ab sin C 2
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13.5 Law of Sines KJ.notebook
April 15, 2015
Find the area of each triangle given: o
a) A = 68 , b = 13, c= 7
b)
223 o
54.2 125
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