What are the dimensions of a 72in television with a 16:9 aspect ratio

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What are the dimensions of a 72in television with a 16:9 aspect ratio

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    2021-10-18T20:06:13+00:00

    Answer:

    Height is 35.3 inches.

    Width is 62.8 inches.

    Dimensions are 62.8 by 35.3.

    Step-by-step explanation:

    We can solve this problem using some simple trigonometry.

    First, we need to calculate the angle of the corner to corner line relative to the base. We use tan⁻¹ to solve for this.

    tan⁻¹(\frac{9}{16})

    29.35775354°

    We can now use this angle to find the side length to hypotenuse ratios. First, we will find the height using sine.

    sin is \frac{opposite}{hypotenuse}

    \frac{x}{72} = sin(29.35775354°) — plug in known info

    \frac{x}{72} = 0.4902612396 — solve

    x = 0.4902612396 × 72 — multiply both sides by 72

    x = 35.29880925

    Height is 35.3 inches.

    Now, we can solve for the width using cosine.

    cos is \frac{adjacent}{hypotenuse}

    \frac{w}{72} = cos(29.35775354°) — plug in known info

    \frac{w}{72} = 0.8715755371 — solve

    w =  0.8715755371 × 72 — multiply both sides by 72

    w = 62.75343867

    w = 62.8 inches

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