I'll do problem 1 to get you started
We have 3 right triangles, meaning that they are similar triangles (you can use the AA similarity theorem to prove this). Because of the similar triangles, we can form the proportion below
50/20 = 20/r
which solves to...
50/20 = 20/r
50r = 20*20
50r = 400
50r = 400/50
r = 8
Now we can use the pythagorean theorem to find the hypotenuse (t) of the smallest right triangle
a^2 + b^2 = c^2
8^2 + 20^2 = t^2
64 + 400 = t^2
464 = t^2
t^2 = 464
sqrt( t^2 ) = sqrt( 464 )
t = sqrt(464)
t = sqrt(16*29)
t = sqrt(16)*sqrt(29)
t = 4*sqrt(29) exact value of t
t = 21.540659 approximate value of t
