\begin{tabular}{l} A ladder leans against the wall of a building. \\ The ladder measures 53 inches and forms an \\ angle of \( 55^{\circ} \) with the ground. How far from \\ the ground, in inches, is the top of the ladder? \\ How far from the wall, in inches, is the base \\ of the ladder? Round to two decimal places \\ as needed. \\ Show your work here \\ ground to top, in inches: \\ base to wall, in inches: \\ \hline\end{tabular}

To find the height of the top of the ladder from the ground and the distance from the wall to the base of the ladder, we can use trigonometric functions. 1. **Height from the ground (opposite side)**: We can use the sine function. \[ \text{Height} = \text{Ladder length} \times \sin(\text{angle}) \] \[ \text{Height} = 53 \times \sin(55^{\circ}) \approx 53 \times 0.8192 \approx 43.42 \text{ inches} \] So, the height from ground to top is approximately **43.42 inches**. 2. **Base to wall (adjacent side)**: We can use the cosine function. \[ \text{Base to wall} = \text{Ladder length} \times \cos(\text{angle}) \] \[ \text{Base to wall} = 53 \times \cos(55^{\circ}) \approx 53 \times 0.5736 \approx 30.40 \text{ inches} \] So, the distance from the wall to the base of the ladder is approximately **30.40 inches**. Final answer: - Ground to top, in inches: **43.42** - Base to wall, in inches: **30.40**