Answer:
[tex]x=2\sqrt{41}[/tex]
[tex]y=39^\circ[/tex]
[tex]z=51^\circ[/tex]
Step-by-step explanation:
In the given right angle triangle.
Using pythagoreous theorem,
[tex]a^2+b^2=c^2[/tex]
where, a=8, b=10 and c=x
[tex]8^2+10^2=x^2[/tex]
[tex]64+100=x^2[/tex]
[tex]x=\sqrt{164}[/tex]
[tex]x=2\sqrt{41}[/tex]
Using trigonometry formula:
[tex]\tan y=\dfrac{8}{10}[/tex]
[tex]y=\tan^{-1}(0.8)[/tex]
[tex]y=39^\circ[/tex]
[tex]\tan z=\dfrac{10}{8}[/tex]
[tex]z=\tan^{-1}(1.25)[/tex]
[tex]z=51^\circ[/tex]
