Given that \(\sin \alpha = \dfrac{3}{5}\) and \(\cos \beta = \dfrac{12}{13}\), prove that one possible value of \(\cos(\alpha + \beta)\) is \(\dfrac{33}{65}\)…

Could we draw a diagram with right-angle triangles and the angles \(\alpha\), \(\beta\) and \(\alpha+\beta\)?

If two sides of a right-angle triangle are \(3\) and \(5\), what is the third side?