The height of the screen is approximately 700 centimeters, correct to the nearest centimeter.
To find the height of the screen (x), we can use the tangent of the viewing angle in a right triangle formed by the viewer (point P), the top of the screen, and the bottom of the screen.
Let x be the height of the screen, and the distances between P and the top and bottom of the screen be 25m and 23m, respectively. The tangent of the viewing angle (18 degrees) is calculated as the ratio of the opposite side to the adjacent side in the right triangle.
tan(18°) = x/25
Solving for x:
x = 25 * tan(18°)
Using trigonometric functions or a calculator, we find x≈7.00 meters.
Now, to convert this result to the nearest centimeter, we multiply by 100: x≈700 cm
Therefore, the height of the screen is approximately 700 centimeters, correct to the nearest centimeter.