Layla leans a 26-foot ladder against a wall so that it forms an angle of \( 61^{\circ} \) with the ground. How high up the wall does the ladder reach? Round your answer to the nearest tenth of a foot if necessary.

To find out how high the ladder reaches up the wall, we can use trigonometry. Specifically, we will use the sine function, which relates the angle of a right triangle to the ratio of the length of the opposite side (the height the ladder reaches on the wall) to the hypotenuse (the length of the ladder). 1. **Identify the known values:** - Length of the ladder (hypotenuse) \( L = 26 \) feet - Angle with the ground \( \theta = 61^{\circ} \) 2. **Set up the equation using the sine function:** \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] Here, the opposite side is the height \( h \) that the ladder reaches on the wall. 3. **Substituting the known values into the equation:** \[ \sin(61^{\circ}) = \frac{h}{26} \] 4. **Rearranging the equation to solve for \( h \):** \[ h = 26 \cdot \sin(61^{\circ}) \] Now, we will calculate \( h \). Calculate the value by following steps: - step0: Calculate: \(26\sin\left(61\right)\) Calculating the height \( h \): \[ h \approx 26 \cdot \sin(61^{\circ}) \approx 26 \cdot 0.8746 \approx 22.7 \text{ feet} \] Thus, the height that the ladder reaches up the wall is approximately \( 22.7 \) feet when rounded to the nearest tenth of a foot.