Question 1:
Use the Pythagorean theorem.
If [tex]c^2\ \textless \ a^2+b^2[/tex], then the angle is acute.
If [tex]c^2=a^2+b^2[/tex], then the angle is right.
If [tex]c^2\ \textgreater \ a^2+b^2[/tex], then the angle is obtuse.
[tex]a=18[/tex]
[tex]b=80[/tex]
[tex]c=81[/tex]
[tex]c^2=6561[/tex]
[tex]a^2+b^2=324+6400=6724[/tex]
[tex]\boxed {c^2\ \textless \ a^2+b^2}[/tex]
Thus, the angle is acute.
Question 2:
Take the square root of the area to get the side length.
[tex] \sqrt{200} = \sqrt{100*2} =10 \sqrt{2} [/tex]
That's the side length. Since we have a 45-45-90 right triangle if we divide the square across its diagonal, we just multiply the side length by the square root of 2 in order to get the diagonal length.
[tex]10 \sqrt{2} * \sqrt{2} [/tex]
[tex]=20[/tex]
Your answer is 20 m. Hope this helps! :)
