How is equation 15.14 derived in the wave speed derivation?

[Fluxthroughme]

With reference to this diagram, my textbook tells me the following:

I am able to follow the rest of the derivation after this point, but I do not understand where equation 15.14 came from? I'm trying to think in terms of small angle approximations, but nothing is really coming of that. Any help is appreciated.

Thanks.

 

[tms]

The equation just says mathematically what the words say.

 

[Fluxthroughme]

The equation just says mathematically what the words say.

I know what the equation says. I don't know where it came from, I.E, I don't know why it is true.

 

[SteamKing]

The rope can only experience tension. Therefore, the slope of the rope at any point must also coincide with the direction of the tension force in the rope.