Question 7323
Let h ft. be the original height of tree.
The remaining upright piece ater the lightning strike is (3/8)h ft.
The broken-off piece is then (5/8)h ft. This forms the hypotenuse of the right triangle, whose base is 40 ft.

Using the Pythagorean theorem, {{{c^2 = a^2 + b^2}}} we can write:

{{{((5/8)h)^2 = ((3/8)h)^2 + (40)^2}}} Subtract {{{(3/8)h^2}}} from both sides.

{{{(1/4)h^2 = 40^2}}} Multiply both sides by (4/1).

{{{h^2 = 40^2(4)}}} Take the square root of both sides.

{{{h = 40(2)}}}

{{{h = 80 ft.}}}