A wooden board is leaning against a house. The base of the board is 10 feet from the base of the house, and the base of the board forms a $35^{\circ}$ angle with the ground. What is the length of the wooden board? Enter your answer, rounded to the nearest tenth, in the box.

Step 1 ：The problem describes a right triangle, where the base of the board is the adjacent side, the height of the house is the opposite side, and the length of the board is the hypotenuse.

Step 2 ：We know the length of the adjacent side (10 feet) and the angle between the adjacent side and the hypotenuse (35 degrees).

Step 3 ：We can use the cosine of the angle to find the length of the hypotenuse. The cosine of an angle in a right triangle is equal to the length of the adjacent side divided by the length of the hypotenuse.

Step 4 ：Therefore, the length of the hypotenuse is equal to the length of the adjacent side divided by the cosine of the angle.

Step 5 ：Let's denote the base as \(b\), the angle as \(\alpha\), and the length of the board as \(L\). We have \(b = 10\) feet and \(\alpha = 35^\circ\).

Step 6 ：First, we need to convert the angle from degrees to radians. We use the formula \(\alpha_{rad} = \frac{\alpha \cdot \pi}{180}\). Substituting the given values, we get \(\alpha_{rad} = 0.6108652381980153\).

Step 7 ：Next, we use the formula for the cosine of an angle in a right triangle, which is \(\cos(\alpha) = \frac{b}{L}\). Solving for \(L\), we get \(L = \frac{b}{\cos(\alpha)}\).

Step 8 ：Substituting the given values into the formula, we get \(L = 12.20774588761456\) feet.

Step 9 ：Rounding to the nearest tenth, we get \(L = 12.2\) feet.

Step 10 ：Final Answer: The length of the wooden board is approximately \(\boxed{12.2}\) feet.