GCSE(H),

The cosine rule can be used for any triangle. The letters relating to the side are opposite the corresponding letters for the angles, i.e. a and A; b and B and c and C.

The rule is:

`a^2 = b^2 + c^2 - 2bc cosA`

Use the cosine rule when all three sides are known, or two sides and an included angle are known.

1. What is the length of BC? Give your answer to 2 decimal places.

Answer: 16.08 cm

Using the cosine rule:

`a^2 = b^2 + c^2 - 2bc cosA`

`a^2 = 12^2 + 14^2 - 2 xx 12 xx 14 xx cos 76`

`a^2 = 144 + 196 - 336 xx 0.24192`

`a^2 = 340 - 81.28512`

`a^2 = 258.71488`

`a = 16.0846`, or 16.08 (2dp)

2. What is the size of the angle *x*? Give your answer to 1 decimal place.

Answer: 67.5ยบ

Using the cosine rule:

`a^2 = b^2 + c^2 - 2bc cosA`

`10^2 = 8^2 + 9^2 - 2 xx 8 xx 9 xx cos A`

`100 = 64 + 91 - 144 xx cos A`

`100 = 155 - 144 xx cos A`

`-55 = -144 xx cos A`

`cos A = 0.3819`

`A = cos^-1 0.3819`

`A = 67.546`, or 67.5 (1dp)

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