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 bo 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

To determine the length of the wooden board, we can use trigonometry, specifically the cosine function. Given: - The distance from the base of the board to the house (adjacent side) is 10 feet. - The angle between the ground and the board is \( 35^{\circ} \). The cosine of the angle is defined as the adjacent side divided by the hypotenuse (the length of the board, which we'll call \( L \)): \[ \cos(35^{\circ}) = \frac{10}{L} \] Solving for \( L \): \[ L = \frac{10}{\cos(35^{\circ})} \] Calculating \( \cos(35^{\circ}) \): \[ \cos(35^{\circ}) \approx 0.8192 \] Now, substitute back to find \( L \): \[ L = \frac{10}{0.8192} \approx 12.2168 \text{ feet} \] Rounding to the nearest tenth: \[ L \approx 12.2 \text{ feet} \] **Answer:** 12.2