Answer:
the measure of the angles are: [tex]{\frac{\pi}{3},\frac{\pi}{6},\frac{\pi}{2}}[/tex]
Step-by-step explanation:
Let the side of the triangle ABC is given by a,b,c.
The measure of the angle is given by as depicted in the figure.
so let [tex]a=\sqrt{6},b=\sqrt{2},c=2\sqrt{2}[/tex]
[tex]A=\arccos(\frac{1}{2}), B=\arccos(\frac{\sqrt{3}}{2}) , C=\arccos (0)[/tex]
[tex]A=\frac{\pi}{3},B=\frac{\pi}{6},C=\frac{\pi}{2}[/tex]
if the base of a triangle is [tex]\sqrt{6}[/tex], then let the base angle be some X.
[tex]\cos (X)=\frac{\sqrt{6}}{2\sqrt{2}}[/tex]
where [tex]\sqrt{6}[/tex] is base and [tex]2\sqrt{2}[/tex] is hypotneuse.
[tex]X=\arccos(\frac{\sqrt{3}}{2})[/tex]
[tex]X=\frac{\pi}{6}[/tex]
so the measure of base angle when base length is [tex]\sqrt{6}[/tex] is [tex]\frac{\pi}{6}[/tex]
