Please help to determine the exact length of the wood

Question

To support a new 5m wall in the construction of a home, the carpenters nail a piece of wood from the top of the wall to the floor, with the piece of wood forming the hypotenuse of a right triangle it makes with the wall and floor. The piece of wood is nailed to the ground such that it makes a 30° angle with the floor. Determine the EXACT length of the piece of wood.

Answer 1

Notice that a 30-60-90 triangle will be used for many, many problems because the sides are x, x√3 and 2x.

Using the Pythagorean Theorem: x² + (x√3)² = (2x)²

or 4x² = 4x²

Since the height (that is, x) is 5m, the exact measure of the board is 10m.