Fabian leans a 26 -foot ladder against a wall. If the ladder reaches 23.4 feet up the wall, what angle does it form with the ground? Round your answer to the nearest tenth of a degree.

To determine the angle that the ladder forms with the ground, we can model the situation using a right triangle where: - **Hypotenuse (Ladder):** 26 feet - **Opposite Side (Height up the wall):** 23.4 feet Let's denote the angle between the ladder and the ground as \( \theta \). ### Using the Sine Function The sine of the angle \( \theta \) is given by: \[ \sin(\theta) = \frac{\text{Opposite Side}}{\text{Hypotenuse}} = \frac{23.4}{26} = 0.9 \] To find \( \theta \), take the inverse sine (arcsin) of 0.9: \[ \theta = \arcsin(0.9) \approx 64.158^\circ \] ### Rounding to the Nearest Tenth Rounding \( 64.158^\circ \) to the nearest tenth of a degree: \[ \theta \approx 64.2^\circ \] **Final Answer:** The ladder forms an angle of approximately 64.2° with the ground.