Law of cosines — Precalculus, what it means and where it is taught
c2 = a2 + b2 - 2abcos C.
Taught in Precalculus.
Where it is taught
Practise this idea
3 questions in the course bank use Law of cosines, in The Law of Sines & Cosines.
Problem 1
Two angles and one side are known. Which rule applies?
- Law of sines
- Law of cosines
- Pythagoras
- Neither
Worked answer
Law of sines
The third angle follows, giving a complete pair
Problem 2
All three sides are known and no angles. Which rule applies?
- Law of cosines
- Law of sines
- Pythagoras
- Neither
Worked answer
Law of cosines
No angle is known, so the sine rule cannot start
Problem 3
A triangle has sides 4, 5 and 6. Find the angle opposite the side of length 6, to the nearest degree.
Worked answer
83
36 = 16+25-2(4)(5)cos C
cos C = 540 = 0.125
C ≈ 83°