# How do you prove the relation between the three interfacial (surface) tensions? [duplicate]

In my textbook, Physics for Class XI—Part II, there's a paragraph which proves a relation among the surface tensions of three interfaces—liquid-air, solid-air and solid-liquid when a liquid comes in contact with a solid. The paragraph goes thus:

We consider the three interfacial tensions at all the three interfaces, liquid-air, solid-air, and solid-liquid denoted by $$S_{la}$$, $$S_{sa}$$, and $$S_{sl}$$, respectively as given in Fig. 10.19 (a) and (b). At the line of contact, the surface forces between the three media must be in equilibrium. From Fig. 10.19 (b) the following relation is easily derived: $$S_{la} \cos\theta + S_{sl} = S_{sa}$$

Even though the relation is 'easily derived', I don't understand how that's been done. It'd be helpful if the derivation is shown, or at least a hint is given.

I'm attaching Fig. 10.19 (a) and (b) for clarity.

PS: It'd also be helpful if it could be made a tad more clear why it's been assumed that the surface forces between the three media must be in equilibrium.