At noon, a tree casts a shadow that is 40 feet long. The distance from the top of the tree to the furthest tip of the shadow is 60 feet.

For this case what we must do is find the height of the tree.
 For this we use the Pythagorean theorem in the following way:
 a ^ 2 + b ^ 2 = c ^ 2
 Where,
 a: height of the tree
 b: base of the triangle (length of the shadow)
 c: hypotenuse (The distance from the top of the tree to the furthest tip of the shadow).
 Substituting we have:
 a ^ 2 + (40) ^ 2 = (60) ^ 2
 Clearing to have:
 a = root ((60) ^ 2 - (40) ^ 2)
 a = 44.72135955
 a = 44.7 feet
 Answer:
 The height of the tree is:
 a = 44.7 feet