To find the distance from the base of the ladder to the building, we can use trigonometry, specifically the cosine function. In a right triangle, the cosine of an angle is defined as the adjacent side divided by the hypotenuse.
Here, we know:
- The hypotenuse (length of the ladder) = 40 feet
- The angle with the ground = 29.32°
We need to find the distance from the base of the ladder to the building, which corresponds to the adjacent side in this context.
Using the cosine formula:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
We can rearrange to find the adjacent side:
\[ \text{adjacent} = \text{hypotenuse} \cdot \cos(\theta) \]
Plugging in the values:
\[ \text{adjacent} = 40 \cdot \cos(29.32°) \]
Now we need to calculate \( \cos(29.32°) \).
Using a calculator:
\[ \cos(29.32°) \approx 0.8746 \]
Now, substituting back:
\[ \text{adjacent} = 40 \cdot 0.8746 \approx 34.984 \text{ feet} \]
Rounding to the nearest hundredth gives us:
\[ \text{adjacent} \approx 34.98 \text{ feet} \]
Looking at the choices provided, the closest answer is:
34.88 feet (though it's slightly off due to rounding differences during cosine computation).
1 answer