For a viewer 103 inches away viewing a 4K image, what is the necessary image height?

To determine the necessary image height for optimal viewing of a 4K image from a distance of 103 inches, we can use a general guideline that suggests a viewing angle of approximately 30 degrees for comfortable viewing of high-resolution content like 4K. To find the height, we can use the trigonometric relationship involving the tangent function.

1. Calculate the height using the tangent of the angle. The formula for calculating the height of the image based on viewing distance (D) and viewing angle (θ) is:

[

\text{Height} = D \times \tan\left(\frac{\theta}{2}\right)

]

2. Setting the optimal angle for 4K content at approximately 30 degrees, we compute:

[

\text{Height} = 103 \times \tan\left(\frac{30}{2}\right)

]

3. Simplifying this:

[

\text{Height} = 103 \times \tan(15)

]

4. The tangent of 15 degrees is approximately 0.2679, leading to:

[

\text{Height} = 103 \times