triangle warm-up can the following side lengths be the side lengths of a triangle?
TRANSCRIPT
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Triangle Warm-up
Can the following side lengths be the side lengths of a triangle?
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Law of Sinesand
Law of Cosines
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• Solving Triangles Flow Chart
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Law of Sines
If you know the measures of two angles and one side of a triangle, you can find the other two sides of the triangle by using the Law of Sines
In other words, if you are given ASA or AAS, use the Law of Sines.
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Let’s Discover the Law of Sines
1) Find h in terms of a and the sine of an angle
2) Find h in terms of b and the sine of an angle
3) Use algebra to show
b
B
a
A sinsin
B
C
A c
ba
h
Use Triangle ABC
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Let’s Discover the Law of Sines
4) Find k in terms of c and the sine of an angle
5) Find k in terms of b and the sine of an angle
6) Use algebra to show
b
B
c
C sinsin
Use Triangle ABC
k
B
C
A c
ba
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Law of Sines
For a triangle with angles A, B, and C and sides of lengths a, b, and c (a opposite A, b opposite B, and c opposite C),
c
C
b
B
a
A sinsinsin
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Example 1
Solve the triangle.
3859B
C
A
b350 cm
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Example 2
Solve the triangle and find the area.
69
B
C
A
150 cm250 cm
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Example 3
Solve the triangle and find the area.
38
21
24
P
A
L
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Law of Cosines
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Law of Cosines
For any triangle with sides of lengths a, b, and c, and with C the angle opposite the
side with length c,
Cabbac cos2222
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Example 4
Solve the triangle and find the area.
36
52 cm
r
45 cm
C R
T
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Example 5
Solve the triangle and find the area.
225 cm
175 cm
250 cm
Q E
D
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