Your friend has built the skate board ramp shown in the figure with sides of 16 in., 63 in., and 65 in. that he claims has disproved the pythagorean theorem. what do you think?

The friend is wrong - According to the Pythagorean Theorm, if c is the hypotenuse and a and b are opposite sides then  c^{2} = a^{2}  +  b^{2} 
if c=65 inches, a=16 inches and b = 63 inches, then
 65^{2} =16 ^{2} +  63^{2}
right hand side of the equation = 256 + 3969 = 4225
left hand side of the equation = 65^{2}= 4225
So we see, left hand side = right hand side
Hence the theorm is proved.