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:

To find the height from the ground to the top of the ladder and the distance from the wall to the base of the ladder, we can use some basic trigonometry, particularly the sine and cosine functions. 1. **Height from the ground to the top of the ladder (opposite side)**: We can use the sine function because we have the angle (55 degrees) and the hypotenuse (the length of the ladder, which is 53 inches). \[ \text{height} = \text{hypotenuse} \times \sin(\text{angle}) = 53 \times \sin(55^{\circ}) \] First, we calculate \(\sin(55^{\circ}) \approx 0.8192\). \[ \text{height} \approx 53 \times 0.8192 \approx 43.46 \text{ inches (rounded to two decimal places)} \] 2. **Distance from the wall to the base of the ladder (adjacent side)**: We can use the cosine function for this calculation. \[ \text{base} = \text{hypotenuse} \times \cos(\text{angle}) = 53 \times \cos(55^{\circ}) \] Now we calculate \(\cos(55^{\circ}) \approx 0.5736\). \[ \text{base} \approx 53 \times 0.5736 \approx 30.39 \text{ inches (rounded to two decimal places)} \] So, the answers are: ground to top, in inches: 43.46 base to wall, in inches: 30.39