Question

Please help thank you

Answer 1

Question 1:

Use the Pythagorean theorem.

If $c^2\ \textless \ a^2+b^2$, then the angle is acute.
If $c^2=a^2+b^2$, then the angle is right.
If $c^2\ \textgreater \ a^2+b^2$, then the angle is obtuse.

$a=18$
$b=80$
$c=81$

$c^2=6561$
$a^2+b^2=324+6400=6724$

$\boxed {c^2\ \textless \ a^2+b^2}$

Thus, the angle is acute.

Question 2:

Take the square root of the area to get the side length.

$\sqrt{200} = \sqrt{100*2} =10 \sqrt{2}$

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.

$10 \sqrt{2} * \sqrt{2}$
$=20$

Your answer is 20 m. Hope this helps! :)