Name: Flosha, Ezckel G. 11 . Date: \( 16 / 12 / 24 \) Direction: Solve all problems neatly ( 40 pts ) A A ladder 12 cm long rests on a vertical wall. If the angle of elevation is \( 30^{\circ} \), find the distance the foot of the ladder is away from the wall. ( 4pts )

To solve the problem, you can visualize the scenario with a right triangle where the ladder acts as the hypotenuse. Given that the angle of elevation is \(30^{\circ}\) and the length of the ladder is 12 cm, you can use basic trigonometry. The formula for the horizontal distance (adjacent side) is given by: \[ \text{distance} = \text{hypotenuse} \times \cos(\text{angle}) \] Applying the values: \[ \text{distance} = 12 \times \cos(30^{\circ}) = 12 \times \left(\frac{\sqrt{3}}{2}\right) = 12 \times 0.866 \approx 10.39 \text{ cm} \] So, the foot of the ladder is approximately 10.39 cm away from the wall. Remember to neatly label your work, showing each step of the calculation for full credit!