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Laws of Sines and Cosines

Concept:

The Pythagorean Theorem is used to solve right triangles, but to solve oblique triangles, the Law of Sines and the Law of Cosines are needed.

Law of Sines

sin A
a
=
sin B
b
=
sin C
c
a
sin A
=
b
sin B
=
c
sin C

Law of Cosines

c2
=
a2
+
b2
-
2ab cos C
b2
=
a2
+
c2
-
2ac cos B
a2
=
b2
+
c2
-
2bc cos A
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Sides:
a
b
c
Angles:
A
B
C
Give exactly 3 pieces of information.

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS

1 2 3 4 5 6
1. Solve the triangle for which
a = 8.919 in., c = 6.427 in., B = 74.80°.
2. Solve: b = 386 cm, c = 258 cm,
C = 68.5°.
3. Find the angles for the triangle with side of length a = 28 m, b = 47 m, and
c = 58 m.
4. Find the remaining elements of the triangle: c = 2798 ft, A = 18.75°,
B = 51.53°.
5. Find the rest of the triangle that has sides a = 29.81 yd, b = 23.76 yd, and angle B = 39.68°.
6. Solve: b = 675 km, A = 35.3°,
B = 52.8°