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The total height of the piece of plywood is 14 feet.

Explanation:

The given triangle has a 5-foot long adjacent side and a 13-foot long hypotenuse. As we have two sides of the triangle, we can solve for the length of the other side by using Pythagoras theorem. Assume the opposite side of the triangle measures x feet.                                          According to Pythagoras theorem, 13 = √(5² + x²)                                     Squaring on both sides we get,                                                                                   169 = 25 + x², x² = 169 - 25 = 144, x = √144 = 12 feet.It is displayed that h is equal to 2 feet more than the opposite side of the triangle.                                                                                                            h = x + 2 = 12 feet + 2 feet = 14 feet.