1. **State the problem:** We have a cinema seating layout with rows A and P and a screen. We want to find: a) The angle of elevation from Row A to the bottom of the screen. b) The angle of depression from Row P to the bottom of the screen. 2. **Identify given information:** - Horizontal distance from Row A to Row P: $23.7$ m - Height from bottom of screen to Row A: $2.5$ m - Vertical height to bottom of screen from ground level at Row P: $6.2$ m - Angle at Row A between horizontal and sloped seats: $10^\circ$ 3. **Find the angle of elevation from Row A to the bottom of the screen:** The vertical height difference from Row A to the bottom of the screen is $6.2 - 2.5 = 3.7$ m. The horizontal distance from Row A to the screen is unknown, but since the screen is vertically aligned near Row A, we assume horizontal distance is zero or negligible, so the angle of elevation is simply the angle formed by the vertical height difference over horizontal distance. However, since the screen is near Row A, the angle of elevation is the angle between the horizontal at Row A and the line to the bottom of the screen, which is vertical, so the angle of elevation is $90^\circ$. But the problem likely expects the angle formed by the line of sight to the bottom of the screen from Row A, considering the seating slope. Alternatively, if the screen is directly above Row A, the angle of elevation is $90^\circ$. 4. **Find the angle of depression from Row P to the bottom of the screen:** The vertical height difference from Row P to the bottom of the screen is $6.2$ m (assuming Row P is at ground level). The horizontal distance from Row P to the screen is $23.7$ m. The angle of depression $\theta$ satisfies: $$\tan(\theta) = \frac{\text{vertical height difference}}{\text{horizontal distance}} = \frac{6.2}{23.7}$$ Calculate $\theta$: $$\theta = \arctan\left(\frac{6.2}{23.7}\right)$$ Using a calculator: $$\theta \approx \arctan(0.2616) \approx 14.7^\circ$$ 5. **Final answers:** a) Angle of elevation from Row A to bottom of screen: $90.0^\circ$ (assuming vertical alignment) b) Angle of depression from Row P to bottom of screen: $14.7^\circ$