Law of Cosines

c^{2} = a^{2} + b^{2} - 2 ab cos C

Relates the three sides of any triangle to the cosine of an included angle. Reduces to Pythagoras when C = 90°.

Step-by-step solved example

A triangle has a = 5 m, b = 7 m, included angle C = 60°. Find side c.

Oblique triangle with sides a, b, c opposite the matching angles.

Answer: c = 6.24 m

0/10 correct

1.If C = 90°, law of cosines becomes

2.Sides 3, 4, included 90°. Opposite side?

3.a = 8, b = 8, C = 60°. Side c?

4.cos C = (a² + b² − c²) / (2ab). If a=b=c then cos C =

5.Obtuse angle C means

6.a = 10, b = 6, C = 120°. c² equals

7.Law of sines is

8.A 6-8-10 triangle is

9.Angle C if a=5, b=5, c=5√2

10.Find cos C for a=7, b=8, c=9