Law of Cosines or Cosine Law

Objective: I know how to use the Law of Cosines or Cosine Law to solve triangles.

The Law of Cosines, for any triangle ABC is

a 2 = b 2 + c 2 – 2bc cos A

Refer to the lesson on the law or cosines or cosine law for more information and examples.

Fill in all the gaps, then press "Check" to check your answers. Use the "Hint" button to get a free letter if an answer is giving you trouble. You can also click on the "[?]" button to get a clue. Note that you will lose points if you ask for hints or clues!
1. Find the length of the third side, to 3 decimal places, and the other two angles, to 1 decimal place, in the following triangles

(a) a = 1, b = 2, C = 30°
c = , A = °, B = °

(b) a = 3, c = 4, B = 50°
b = , A = °, C = °

(c) b = 5, c = 10, A = 30°
a = , B = °, C = °

2. Find the angles (to 1 decimal place) in the following triangles

(a) a = 2, b = 3, c = 4
A = °, B = °, C = °

(b) a = 1, b = 1, c = 1.5
A = °, B = °, C = °

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