Boris is sitting in a movie theater, 8 meters from the screen. The angle of elevation from his line of sight to the top of the screen is $11^{\circ}$, and the angle of depression from his line of sight to the bottom of the screen is $51^{\circ}$. Find the height of the entire screen. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale.

Step 1 ：Given that Boris is sitting in a movie theater, 8 meters from the screen. The angle of elevation from his line of sight to the top of the screen is $11^{\circ}$, and the angle of depression from his line of sight to the bottom of the screen is $51^{\circ}$. We are to find the height of the entire screen.

Step 2 ：We can solve this problem using trigonometry. We can break down the problem into two right triangles. The first triangle is formed by Boris, the top of the screen, and the point directly in front of Boris on the ground. The second triangle is formed by Boris, the bottom of the screen, and the point directly in front of Boris on the ground.

Step 3 ：We can use the tangent of the angles to find the height of the screen. The tangent of an angle in a right triangle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the screen and the adjacent side is the distance from Boris to the screen.

Step 4 ：We can calculate the height of the top and bottom parts of the screen separately using the formula: \(\text{height} = \tan(\text{angle}) \times \text{distance}\)

Step 5 ：Let's calculate the height of the top part of the screen: \(\text{height}_{\text{top}} = \tan(11^{\circ}) \times 8 = 1.5550424731017478\) meters

Step 6 ：Next, calculate the height of the bottom part of the screen: \(\text{height}_{\text{bottom}} = \tan(51^{\circ}) \times 8 = 9.879177252280412\) meters

Step 7 ：Finally, add the two heights together to get the total height of the screen: \(\text{total height} = \text{height}_{\text{top}} + \text{height}_{\text{bottom}} = 11.4\) meters

Step 8 ：Final Answer: The height of the entire screen is \(\boxed{11.4}\) meters.