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To solve an oblique triangle means to
find the lengths of its sides and the
measurements of its angles.
Theorem Law of Sines
For a triangle with sides a , b, c and opposite
angles , , , respectively,
sin sin sin
a
b
c
We use the Law of Sines to solve CASE 1
(SAA or ASA) and CASE 2 (SSA) of an
oblique triangle. The Law of Cosines is
used to solve CASES 3 and 4.
CASE 3: Two sides and the included
angle are known (SAS).
CASE 4: Three sides are known (SSS).
Theorem Law of Cosines
For a triangle with sides a , b, c and opposite
angles , , , respectively.
c a b 2ab cos
2
2
2
b a c 2ac cos
2
2
2
a b c 2bc cos
2
2
2
In c a b 2ab cos , what value for gives the
Pythagorea
n theorem?(1) 0 (2) 30 (3) 45 (4) 60 (5) 90
2
2
2
Solve the triangle: b 3, c 4, 40 (SAS)
3
a
40
4
a b c 2bc cos
2
2
2
a 3 4 234 cos 40
2
a 6.614933365
2
2
2
a 2.57
3
2.57
2
2
2
b a c 2ac cos
40
4
2
2
2
a c b
cos
2ac
6.6149 4 3
0.6622
2(2.57)(4)
2
2
48.5
180 40 48.5
915
.
Solve the triangle: a 3,b 5, c 7 (SSS)
3
5
7
2
2
2
a b c 2bc cos
5 7 3
cos
2(5)(7)
2
2
2
b c a
65 13
cos
cos
2bc
70 14
218
.
2
2
2
5
3
a c b
cos
2ac
2
2
218
.
2
7
2
2
2
3 7 5
33 11
2(3)(7)
42 14
38.2
180 21.8 38.2 120