A ladder which is 13m long is made to rest on a vertical pole which is 5m away from the foot of the ladder. How far up the pole is the ladder

Answer 1

Just good ol' Pythagoras.
You might recognize the 5-12-13 right angled triangle, if not

x^2 + 5^2 = 13^2
x^2 = 169 - 25
x^2 = 144
x = √144 = 12

btw, this ladder is not leaning according to standard safety codes
should be appr 4:1, this is 12:5 , great danger of slipping