you'd use the pythagorean theorem.
a^2+b^2=c^2
a is the first leg, b is the second leg, and c is the third leg.
10^2+13^2=c^2
100+169=c^2
269=c^2
take the square root of both sides
16.4=c
16.4cm is your answer!
I would tell her that her prediction is inaccurate because it isn’t guaranteed that the coin will land on both sides an equal amount of times. It’s possible that the coin could land heads up more often than it could land tails up or the other way around.
If you want the height of the crate it's volume / base area = 48/16 = 3 feet.
If you look in a table of sines, you find that sin(θ) = 0.45 corresponds to an angle of about 26°45', so is nearest to 27°.