The law of cosines states that, if you know two sides of a triangle and the angle between them (let's call them [tex]a,b,\alpha[/tex], then the third side [tex] c [/tex] is given by the following formula:
[tex] c^2 = a^2+b^2-2ab\cos(\alpha) [/tex]
You may have noticed that this formula strongly resembles the Pythagorean theorem. In fact, this is a generalization, since the Pythagorean theorem only works for right triangles, where the cosine part is zero and vanishes.
Anyways, plugging the values from your particular case we have
[tex] c^2 = 49+64-2\cdot7\cdot8\cos(32) \approx 18.02 [/tex]
This means that [tex] c = \sqrt{18.02} \approx 4.24 [/tex]
Which rounded to the nearest tenth gives 4.2
