If a 5ft post casts an 8ft shadow at the same time that a nearby tree casts a 48ft shadow how tall is the tree

Here we would use the idea that the post and its shadow form a triangle and the tree and its shadow form a triangle and the side lengths of these two triangles are of the same ratio, ie. if the height of the tree is given by h then:
5/8 = h/48
h = 48*(5/8)
h = 6*5 = 30
Thus the tree is 30 ft tall