Create a question that can be solved using the cosine law. Solve your question and show your work.

Question:
In triangle ABC, the sides are given as follows: [tex]\( a = 7 \)[/tex] cm, [tex]\( b = 9 \)[/tex] cm, and the angle between them [tex]\( \theta = 60^\circ \)[/tex]. Find the length of side [tex]\( c \)[/tex].

Solution:
To find the length of side [tex]\( c \)[/tex], we use the cosine law:

[tex]\[ c^2 = a^2 + b^2 - 2ab \cos(\theta) \][/tex]

Plug in the values:

[tex]\[ c^2 = 7^2 + 9^2 - 2 \cdot 7 \cdot 9 \cdot \cos(60^\circ) \][/tex]

Since [tex]\(\cos(60^\circ) = 0.5\)[/tex]:

[tex]\[ c^2 = 49 + 81 - 2 \cdot 7 \cdot 9 \cdot 0.5 \][/tex]
[tex]\[ c^2 = 49 + 81 - 63 \][/tex]
[tex]\[ c^2 = 67 \][/tex]

Take the square root of both sides to find [tex]\( c \)[/tex]:

[tex]\[ c = \sqrt{67} \][/tex]

Therefore, the length of side [tex]\( c \)[/tex] is [tex]\( \sqrt{67} \)[/tex] cm.