April 11, 2013
Warm Ups 10-4
A faster way of solving the classic "how
tall is the hill ? " problem
1. old way: with a system. write two
equations in x and h. Solve to find h
h
50
300 yd
70
2. new way: find all missing angles. Use
them with the law of sines to find h.
x
April 11, 2013
The Law Of Sines has so far solved ASA and AAS cases, but
not AAA, SSS, or SAS cases. Nothing solves AAA cases
because they aren't unique. SSS and SAS can be solved, but
we will need a different law for that. There is one case we
still need to look at: the ambiguous case SSA.
70
60
110
50
40
B
Solve
4
A
6
100
80
110
120
70
120
130
60
140
50
140
40
0°
150
150
30
20
160
160
a
10
0
20
20
170
10
180
0
170
180
C
0
127
90
100
130
30
0
0°
90
80
1
0°
2
3
1
4
5
2
6
7
8
3
9
10
4
11
12
13
5
14
15
April 11, 2013
Switch the 4 and 6 around, and let's solve this SSA triangle
B
6
A
a
20
4
C
30
40
20
150
10
140
50
130
60
120
160
0
70
80
110
90
100
170
100
90
180
80
110
41°
70
120
60
50
40
30
130
140
150
20
160
10
170
0
180
0
0
176
0°
1
0°
2
3
1
4
5
2
6
7
8
3
9
10
4
11
12
13
5
14
15
April 11, 2013
And some SSA aren't even contructable
Solve the SSA triangle below
2
20
10
70
60
110
50
40
80
100
90
90
100
80
110
120
70
120
130
60
130
140
30
140
50
40
0°
150
30
150
20
160
160
10
0
0
0
58
0°
1
0°
2
3
1
4
20
170
10
180
0
5
2
6
7
8
3
9
10
4
11
12
13
5
14
15
170
180
April 11, 2013
On page 295 in IB book, there is a summary of how many triangle
you can draw for the SSA case---0, 1 ,or 2. But you need to know
the height of the triangle. It is easier to always just try to find a
second set of answers. You'll know quickly if there is 0,1,or 2
answers. That is why they call SSA the ambiguous case, and we use
the Law of Sines to solve them.
April 11, 2013
Drag the following triangles under their proper headings
ASA
solvable by
Law of Sines
AAS
solvable by
Law of Sines
10
2
15
10
SSS
solvable
but not by
Law of Sines
9
14
15
12
4
6
13
7
10
15
26
4
SAS
AAA
solvable
not
but not by
solvable
Law of Sines
12
4
23
6
80
9
13
12
88
SSA
ambiguous
case
0, 1, or 2
triangles
April 11, 2013
Law of Sines solves ASA, AAS, and SSA , the ambiguous case.
Make sure you can find all of the triangles in the ambiguous
case. Know how to do bearing problems, and how to interpret
angles of elevation and depression.
Know how to find areas of non right triangles
4
100o
14
6
50
6
70
4
7
Next week we will learn how to solve SSS and SAS cases.
April 11, 2013
#10-4 p. 298 2-10 even, p. 297 1-3
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