To find the distance \( x \) between the foot of the ladder and the base of the building using the cosine function, we can use the following relationship in a right triangle:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this situation:
- The hypotenuse is the length of the ladder, which is 16 feet.
- The angle of elevation \( \theta \) is 55°.
- The adjacent side (the distance from the foot of the ladder to the wall) is \( x \).
Using the cosine function: \[ \cos(55^\circ) = \frac{x}{16} \]
To find \( x \), we can rearrange the equation: \[ x = 16 \cdot \cos(55^\circ) \]
Now, we calculate \( \cos(55^\circ) \): \[ \cos(55^\circ) \approx 0.5736 \]
Next, plug this value into the equation for \( x \): \[ x \approx 16 \cdot 0.5736 \approx 9.1776 \]
Rounding to the nearest hundredth: \[ x \approx 9.18 \]
Thus, the distance between the foot of the ladder and the base of the building is approximately \( \boxed{9.18} \) feet.
5 answers