To find the distance from the base of the board to the wall, we can use the cosine function from trigonometry. The cosine of an angle in a right triangle is defined as the adjacent side divided by the hypotenuse.
In this scenario:
- The hypotenuse is the length of the board, which is 10 feet.
- The angle with the ground is 60 degrees.
- The side adjacent to the angle (the distance from the wall) can be found using the cosine function.
Using the cosine function:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
Here, \(\theta = 60^\circ\), and we can denote the distance from the wall as \(d\). Thus:
\[ \cos(60^\circ) = \frac{d}{10} \]
We know that:
\(\cos(60^\circ) = \frac{1}{2}\)
Now we can substitute this value into the equation:
\[ \frac{1}{2} = \frac{d}{10} \]
Next, solve for \(d\):
\[ d = 10 \cdot \frac{1}{2} = 5 \text{ feet} \]
Therefore, the distance from the base of the board to the wall is 5 feet.