In the triangle $ABC$, $AB = 11$ cm, $BC = 7$ cm and $CA = 8$ cm - Edexcel - A-Level Maths Pure - Question 7 - 2011 - Paper 3

To find angle $C$, we will use the Law of Cosines:

$c^2 = a^2 + b^2 - 2ab \cos C$

Substituting the known values:

$7^2 = 11^2 + 8^2 - 2 \times 11 \times 8 \cos C$

Calculating the squares:

$49 = 121 + 64 - 176 \cos C$

Combining:

$49 = 185 - 176 \cos C$

Rearranging gives us:

$176 \cos C = 185 - 49$ $176 \cos C = 136$

Now divide both sides by 176:

$\cos C = \frac{136}{176} = 0.77273$

Calculating angle $C$:

$C = \cos^{-1}(0.77273) \approx 0.6947 \text{ radians}$

Rounding to 3 significant figures:

$C \approx 0.695 \text{ radians}$