Question 1:
Let's use the Pythagorean theorem.
[tex]a=12[/tex]
[tex]b=15[/tex]
[tex]c=20[/tex]
If [tex]c^2\ \textless \ a^2+b^2[/tex], then the angle is acute.
If [tex]c^2\ \textgreater \ a^2+b^2[/tex], then the angle is obtuse.
If [tex]c^2=a^2+b^2[/tex], then the angle is right.
[tex]c^2=400[/tex]
[tex]a^2+b^2=144+225=369[/tex]
[tex]\boxed{c^2\ \textgreater \ a^2+b^2}[/tex]
Thus, the angle is obtuse.
Question 2:
Use the Pythagorean theorem.
[tex]a=b=8[/tex]
[tex]c=?[/tex]
[tex]a^2+b^2=c^2[/tex]
[tex]8^2+8^2=c^2[/tex]
[tex]c^2=64+64[/tex]
[tex]c^2=128[/tex]
[tex]c= \sqrt{128} [/tex]
[tex]c= \sqrt{64*2} [/tex]
[tex]\boxed{c=8 \sqrt{2} }[/tex]
That's your answer.
Hope this helps! :)
