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(Physics 2, Waves) Why does tan$\tan(theta\theta) = dy/dxdx$?

In the following example:

enter image description here

At the very last step, how does the author get that tan(theta) = dy/dx$\tan(\theta) = dy/dx$? To which dy$dy$ and dx$dx$ is this referring to? It can't be the same dx$dx$ that is labelled in the diagram, can it? Where do these dy$dy$ and dx$dx$ come from?

(Physics 2, Waves) Why does tan(theta) = dy/dx?

In the following example:

enter image description here

At the very last step, how does the author get that tan(theta) = dy/dx? To which dy and dx is this referring to? It can't be the same dx that is labelled in the diagram, can it? Where do these dy and dx come from?

(Physics 2, Waves) Why does $\tan(\theta) = dy/dx$?

In the following example:

enter image description here

At the very last step, how does the author get that $\tan(\theta) = dy/dx$? To which $dy$ and $dx$ is this referring to? It can't be the same $dx$ that is labelled in the diagram, can it? Where do these $dy$ and $dx$ come from?

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(Physics 2, Waves) Why does tan(theta) = dy/dx?

In the following example:

enter image description here

At the very last step, how does the author get that tan(theta) = dy/dx? To which dy and dx is this referring to? It can't be the same dx that is labelled in the diagram, can it? Where do these dy and dx come from?