[tex]\text{We know that,}\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\text{For}~ \angle1,\\\\~~~~~~\cos \angle 1 = \dfrac bc\\\\\\\implies \cos \angle 1 = \dfrac 35\\\\\\\implies \angle 1 = \cos^{-1} \left( \dfrac 35 \right)\\\\\\\implies \angle 1 = 53.13^{\circ}\\\\\\\text{For} ~ \angle 2,\\\\~~~~~~~\cos \angle 2 = \dfrac ac\\\\\\[/tex]
[tex]\implies \cos \angle 2 = \dfrac 45\\\\\\\implies \angle 2 =\cos^{-1} \left( \dfrac 45 \right)\\ \\\\\implies \angle 2 = 36.86^{\circ}[/tex]
[tex]\text{Hence,}~~ m\angle 1 = 53.13^{\circ}~~ \text{and}~~ m\angle 2 =36.86^{\circ}.[/tex]
